Gruber's Complete SAT Guide 2009

Gruber_FNLcvr_SAT09_Updated:Layout 1 5/23/08 11:40 AM Page 1 THE MOST TRUSTED AND EFFECTIVE SAT* PREP GUIDE WHAT THE...

Author: Gary Gruber

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THE MOST TRUSTED AND EFFECTIVE SAT* PREP GUIDE WHAT THE MEDIA IS SAYING:

“His methods make the questions seem amazingly simple to solve.”—Library Journal “Dr. Gruber knows the ins and outs of the SAT.” —Los Angeles Times WHAT STUDENTS, PARENTS, AND EDUCATORS ARE SAYING:

“The work that Gary Gruber does should be given to every student and every teacher.” —Dr. Shirley Thornton, former Deputy Superintendent, California State Department of Education

“GARY GRUBER IS THE LEADING EXPERT ON THE SAT” — HOUSTON CHRONICLE

“I’ve gone through almost all the SAT books I can get a hold of, and so far the best is the Gruber’s SAT book. I wish I could have found it earlier.” —Online review

“In regards to the breadth and quality of material offered, the difference between Gruber’s and other publications is quite astonishing. Indeed, only Gruber’s deserves the highest recommendation in SAT preparation.” —Online review GET THE SKILLS THAT UNLOCK THE ANSWERS

With the explanation to a question, you can answer that one question. With the Gruber strategies, you can answer thousands of questions! These strategies show you how to think about problems instead of trying to solve each one individually, and can be used consistently on every SAT test. USE THE MOST TRUSTED METHODS

• More schools use Dr. Gruber’s books for SAT courses than any other SAT books. • PBS chose Dr. Gruber to train teachers nationally to improve the nation’s SAT scores. • National learning centers, state agencies, and state education departments have contracted with Dr. Gruber to improve SAT scores and critical thinking ability.

• Essential Strategies for Writing, Vocab, Math, and Critical Reading • And Everything Else You Need

Study Aids/Reference www.sourcebooks.com

$19.95 U.S. $21.99 CAN £10.99 UK

ISBN-13: 978-1-4022-1202-4 ISBN-10: 1-4022-1202-X

www.sourcebookscollege.com

12th Edition

* ® SAT is a registered trademark of the College Entrance Examination Board, which was not involved in the production of, and does not endorse, this book.

GRUBER’S COMPLETE *

SAT GUIDE 2009 “THE BEST BOOK ON THE SAT.” —CBS RADIO

12th Edition

THE EASIEST, FASTEST WAY TO IMPROVE YOUR SCORE

• Unique Diagnostic Test Shows You Why You Got Questions Wrong—And How to Get Them Right

EFFECTIVE STUDY TOOLS THAT ARE ACTUALLY FUN • The 101 Most Important Math Questions You Need to Know

• The Gruber 150,000-Word Vocabulary Builder

• The World’s Shortest SAT Test (16 Questions)

• Inside Info on How SAT Questions Are Created

• The 291 Most Important SAT Words

• Student-Praised Writing, Vocab, Math, and

• Proven Strategies for Solving Problems Quickly

Reading Sections

• Tons of Practice SAT Questions, Each Question

• 5 Full-Length SAT Practice Tests

EAN

Gary R. Gruber, PhD, is recognized nationally as the leading expert on the SAT, test-taking methods, and critical thinking skills. His books on test taking and critical thinking skills have sold more than 7 million copies. Visit www.drgarygruber.com.

“GARY GRUBER IS THE LEADING EXPERT ON THE SAT” — HOUSTON CHRONICLE

*

EVERYTHING YOU NEED TO STUDY TO GET THE TOP SCORE

• Five Full-Length SAT Practice Tests • An Extensive Vocabulary Builder • Advice on Tackling the Essay Section

— CBS RADIO

2009 SAT GUIDE

“With the aid of your books, my scores improved so dramatically that I am now anticipating acceptance into schools that I was reluctant to even apply to.”—Lauren Frasciello, Princeton, New Jersey

MORE THAN 7 MILLION GRUBER BOOKS SOLD!

GRUBER’S COMPLETE

“Gary Gruber is the most prominent guru of SAT preparation.”—Chicago Tribune

“THE BEST BOOK ON THE SAT.”

Explained in Detail and Linked to a Gruber Strategy or Basic Skill

FEATURES THE EXCLUSIVE GRUBER SYSTEM THAT HAS RAISED ACTUAL SAT SCORES BY MORE THAN 600 POINTS!

GARY R. GRUBER, PHD

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GRUBER’S COMPLETE

SAT

*

12th Edition

GUIDE 2009 *SAT is a registered trademark of the College Entrance Examination Board. The College Entrance Examination Board is not associated with and does not endorse this book.

Gary R. Gruber, PhD

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Copyright © 2008 by Gar y R. Gruber Cover design © 2008 by Sourcebooks, Inc. Sourcebooks and the colophon are registered trademarks of Sourcebooks, Inc. All rights reserved. No part of this book may be reproduced in any form or by any electronic or mechanical means including information storage and retrieval systems—except in the case of brief quotations embodied in critical articles or reviews—without permission in writing from its publisher, Sourcebooks, Inc. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold with the understanding that the publisher is not engaged in rendering legal, accounting, or other professional service. If legal advice or other expert assistance is required, the services of a competent professional person should be sought. —From a Declaration of Principles Jointly Adopted by a Committee of the American Bar Association and a Committee of Publishers and Associations Published by Sourcebooks, Inc. P.O. Box 4410, Naperville, Illinois 60567-4410 (630) 961-3900 Fax: (630) 961-2168 www.sourcebooks.com Cataloging-in-Publication data is on file with the publisher.

Printed and bound in Canada WC 10 9 8 7 6 5 4 3 2 1

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Recent and Forthcoming Study Aids from Dr. Gary Gruber Include: Gruber’s Essential Guide to Test Taking: Grades 6-9 Gruber’s Essential Guide to Test Taking: Grades 3-5 Gruber’s SAT 2400 Gruber’s SAT Math Workbook Gruber’s SAT Reading Workbook Gruber’s SAT Writing Workbook

www.sourcebooks.com www.drgarygruber.com

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IMPORTANT NOTE ABOUT THIS BOOK AND ITS AUTHOR • v

Important Note About This Book and Its Author

This book is the most up-to-date and complete book on the current SAT. EVERY EXAM is patterned after the SAT, and all the strategies and techniques deal with the SAT. The SAT incorporates all the Gruber Critical Thinking Strategies. This book was written by Dr. Gary Gruber, the leading authority on the SAT, who knows more than anyone else in the test-prep market exactly what is being tested for in the SAT. In fact, the procedures to answer the SAT questions rely more heavily on the Gruber Critical Thinking Strategies than ever before, and this is the only book that has the exact thinking strategies you need to use to maximize your SAT score. Gruber’s SAT books are used more than any other books by the nation’s school districts and are proven to get the highest documented school district SAT scores. Dr. Gruber has published more than 30 books with major publishers on test-taking and critical thinking methods, with over 7 million copies sold. He has also authored over 1,000 articles on his work in scholarly journals and syndicated nationally in newspapers, has appeared on numerous television and radio shows, and has been interviewed in hundreds of magazines and newspapers. He has developed major programs for school districts and for city and state educational agencies for improving and restructuring curriculum, increasing learning ability and test scores, increasing motivation and developing a “passion” for learning and problem solving, and decreasing the student dropout rate. For example, PBS (Public Broadcasting System) chose Dr. Gruber to train the nation’s teachers on how to prepare students for the SAT through a national satellite teleconference and videotape. His results have been lauded throughout the country from all walks of life. Dr. Gruber is recognized nationally as the leading expert on standardized tests. It is said that no one in the nation is better at assessing the thinking patterns of “how” a person answers questions and providing the mechanism to improve the faulty thinking approaches. SAT score improvements by students using Dr. Gruber’s techniques have been the highest in the nation. Gruber’s unique methods have been and are being used by Public Television (PBS), the nation’s learning centers, international encyclopedias, school districts throughout the country, in homes and workplaces across the nation, and by a host of other entities. His goal and mission is to get people’s potential realized and the nation “impassioned” with learning and problem solving so that they don’t merely try to get a “fast” uncritical answer, but actually enjoy and look forward to solving the problem and learning. For more information on Gruber courses and additional Gruber products, visit www.drgarygruber.com.

Important: Many books do not reflect the current SAT questions. Don’t practice with questions that misrepresent the actual questions on the SAT. For example, the math questions created by the test makers are oriented to allow someone to solve many problems without a calculator as fast as with one and some faster without a calculator. This book reflects the SAT more accurately than any other commercial book, and the strategies contained in it are exactly those needed to be used on the SAT. It is said that only Dr. Gruber has the expertise and ability to reflect the exam far more closely than any competitor! Don’t trust your future with less than the best material.

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THE AUTHOR HAS SOMETHING IMPORTANT TO TELL YOU • vii

The Author Has Something Important to Tell You About How to Raise Your SAT Score

What Are Critical Thinking Skills? First of all, I believe that intelligence can be taught. Intelligence, simply defined, is the aptitude or ability to reason things out. I am convinced that you can learn to think logically and figure things out better and faster, particularly in regard to SAT Math and Verbal problems. But someone must give you the tools. Let us call these tools strategies. And that’s what Critical Thinking Skills are all about—strategies.

Learn the Strategies to Get More Points The Critical Thinking Skills (beginning on page 59) will sharpen your reasoning ability so that you can increase your score up to 300 points on each part of the SAT. These Critical Thinking Skills—5 General Strategies, 19 Math Strategies, and 16 Verbal Strategies—course right through this book. The Explanatory Answers for the 5 Practice Tests in the book direct you to those strategies that may be used to answer specific types of SAT questions. We can readily prove that the strategies in Part 2 of this book are usable for more than 90 percent of the questions that will appear on your SAT. Each additional correct answer gives you approximately 10 points. It is obvious, then, that your learning and using the 40 easy-to-understand strategies in this book will very likely raise your SAT score substantially.

Are the Practice Tests in This Book Like an Actual SAT? If you compare any one of the 5 Practice Tests in this book with an actual SAT, you will find the book test very much like the actual test in regard to format, question types, and level of difficulty. Compare our book tests with one of the official tests, published by the College Board!

Building Your Vocabulary Can Make a Big Difference on Your Test Although Antonyms no longer appear on the SAT, Vocabulary will still be tested, especially on Sentence Completions, and Reading Comprehension. This book includes four vital sections to build your vocabulary:

1. 2. 3. 4. 5.

3,400 Word List 100 Vocabulary Tests 366 Latin and Greek roots, prefixes, and suffixes The 291 Most Important/Frequently Used SAT Words The Hot Prefixes and Roots

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• THE AUTHOR HAS SOMETHING IMPORTANT TO TELL YOU If you have time, it is important for you to study this word-building instructional material. You will find that many, many words in the 3,400 Word List will actually show up in the Sentence Completion and Reading Comprehension sections of the Verbal part of your SAT. We repeat that each additional correct answer adds approximately 10 points to your score. Knowing the meanings of the words in the 3,400 Word List will, therefore, help you considerably to “rake in” those precious points.

Study the 366 Latin and Greek Roots, Prefixes, and Suffixes We have developed a list of roots, prefixes, and suffixes which contains the 50 prefixes and roots that give you the meaning of more than 150,000 words. Learning all 366 will increase your vocabulary immensely. You may also wish to study the Hot Prefixes and Roots in Appendix A.

Study the 291 Most Important/Frequently Used SAT Words We have developed a list of most frequently used words and their opposites related to specific categories for easy memorization. Study these words.

Study the Mini-Math Refresher If you believe you are weak in the basic math skills area, study the Mini-Math Refresher. The material in the section is keyed to the Complete Math Refresher section for more complete instruction.

Take the 101 Most Important Math Questions Test To see what are your weak basic math skills areas, take the 101 Most Important Math Questions Test and look at the solutions to the questions. The questions are keyed to the Complete Math Refresher so you can further brush up on your weak areas by referring to those pages in the Complete Math Refresher part for those questions you missed.

The Explanatory Answers to Questions Are Keyed to Specific Strategies and Basic Skills The Explanatory Answers in this book are far from skimpy—so unlike those of other SAT books. Our detailed answers will direct you to the strategy that will help you to arrive at a correct answer quickly. In addition, the Math solutions in the book refer directly to the 150-page Math Refresher section, particularly useful in case your Math skills are “rusty.”

Lift That SAT Score By using the material in this book, that is, by taking the tests, learning the specific strategies, refreshing your basic skills, etc., as described above, you should increase your SAT score substantially. —Gar y Gruber

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Contents

INTRODUCTION

xiii

I. Important Facts About the SAT/ xiii II. The Inside Track on How SAT Questions Are Developed and How They Vary from Test to Test / xx III. What Are Critical Thinking Skills? / xxi IV. Strategies for Women / xxiii

V. Multi-Level Approaches to Solution of Problems / xxiv VI. A Four-Hour Study Program for the SAT / xxvii VII. Longer-Range Study Program and Helpful Steps for Using This Book / xxviii VIII. Format of the SAT / xxix

PA R T 1

STRATEGY DIAGNOSTIC TEST FOR THE SAT

1

Directions for Taking the Diagnostic Test / 2

Section 2: Math Ability / 12

Strategy Diagnostic Test Answer Sheet / 3

Strategy Diagnostic Test Answer and Diagnostic Table (Keyed to Strategies in book) / 18

Section 1: Verbal Ability / 4

PA R T 2

THE SHORTEST SAT TEST—16 QUESTIONS TO APPROXIMATE YOUR SAT SCORE 23 Verbal (Critical Reading) / 24

Answers / 27

Math / 25

Shortest SAT Test: What You Did Wrong, Explanatory Answers and Scoring, Strategies and Basic Skills Needed to Improve / 28

Writing / 26

PA R T 3

THE 101 MOST IMPORTANT MATH QUESTIONS YOU NEED TO KNOW HOW TO SOLVE 101 Math Questions Answer Sheet / 30

Basic Skills Math Diagnosis / 47

101 Math Questions Test / 32

Solutions, Generalizations, Rules / 48

101 Math Questions: Answers / 45

29

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x • CONTENTS

PA R T 4

STRATEGY SECTION

59

5 General Strategies / 60

What Reading Comprehension Questions Ask / 125

35 Easy-to-Learn Strategies / 62

Getting Involved with the Passage / 125

How to Learn the Strategies / 62

Introductory Passage 1 / 126

Important Note on the Allowed Use of Calculators on the SAT / 62

Breakdown and Underlining of Passage / 126

Important Note on Math Questions on the SAT / 63

How to Answer Reading Comprehension Questions Most Effectively / 127

The Grid-Type Math Question / 63


Use of a Calculator in the Grid-Type Question / 67


19 Math Strategies / 69

Summary / 132

16 Verbal (Critical Reading) Strategies / 117

About the Double-Reading Passages / 132

4 Sentence Completion Strategies / 118

9 Reading Comprehension Strategies / 133

Critical Reading Strategies / 125

3 Vocabulary Strategies / 148

PA R T 5

MINI-MATH REFRESHER

155 PA R T 6

COMPLETE SAT MATH REFRESHER

165

Session #1—Fractions, Decimals, Percentages, etc. / 168

Session #3—Area, Perimeter, and Volume Problems / 219

Fractions, Decimals, Percentages / 168

Area, Perimeter, and Volume Problems / 219

Deviations / 171

Practice Test 3 / 227

Ratios and Proportions / 172

Answer Key for Practice Test 3 / 236

Variations / 173

Answers and Solutions for Practice Test 3 / 236

Comparison of Fractions / 173

Session #4—Algebra Problems / 243


Algebraic Properties / 243


Equations / 244


Algebra of Graphs / 246

Session #2—Rate Problems / 192

Inequalities / 253

Word Problem Setup / 192

Exponents and Roots / 257

Distance and Time / 194


Work / 195


Mixture / 196


Cost / 196

Session #5—Geometr y Problems / 274


Basic Definitions / 274


Triangles / 276


Properties of Triangles / 277

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CONTENTS • xi

Four-Sided Figures / 280

Session #7—Tables, Charts, and Graphs / 326

Many-Sided Figures / 281

Charts and Graphs / 326

Circles / 281

Tables and Charts / 326


Graphs / 327


Bar Graphs / 328


Circle Graphs / 329

Session #6—Miscellaneous Problems / 304 Averages, Medians, and Modes / 304

Line Graphs / 330 Practice Test 7 / 331

Series / 305

Session #8—Modern Math / 337

Properties of Integers / 306

Sets / 337

Approximations / 308

Relations / 338

Combinations / 310

Solution Sets / 338

Probability / 311

Axioms / 339

The Absolute Value Sign / 311

Closed Sets / 339

Functions / 311

Mathematical Symbols / 339


Practice Test 8 and Solutions / 340

Answer Key for Practice Test 6 / 320 Answers and Solutions for Practice Test 6 / 320

PA R T 7

VOCABULARY BUILDING THAT IS GUARANTEED TO RAISE YOUR SAT SCORE 347 Knowing Word Meanings Is Essential for a Higher SAT Score / 348

A List of SAT Words Appearing More Than Once on Actual SAT Exams / 357

8 Steps to Word Power / 349

The 291 Most Important/Frequently Used SAT Words and Their Opposites / 359

The Gruber Prefix-Root-Suffix List That Gives You the Meanings of Over 150,000 Words / 352

The Gruber SAT 3,400 Word List / 363

Roots / 353

100 Tests to Strengthen Your Vocabulary / 415

Prefixes / 355

Answers to Vocabulary Tests / 458

Suffixes / 356

PA R T 8

GRAMMAR AND USAGE REFRESHER The Parts of Speech / 463

Mood and Voice / 497

Clauses and Phrases / 466

Modifiers—Adjectives, Adjective Phrases and Clauses / 500

The Sentence and Its Parts / 469 Verbs / 475 Nouns and Pronouns / 479 Subject-Verb Relationship / 486 Tense / 489 Verbals / 493

461

Modifiers (continued)—Adverbs, Adverbial Phrases and Clauses / 506 Connectives / 510 Correct Usage: Choosing the Right Word / 515 Grammar and Usage Index / 519

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xii • CONTENTS

PA R T 9

THE SAT WRITING TEST

523

The SAT Writing Section / 524

Other Types of Questions on the SAT Writing Test / 539

Content of the Writing Test / 524

Identifying Errors / 539

The Essay on the SAT Writing Test / 525

Sample Questions with Answers / 539

The SAT Essay Scoring Guide / 528

Improving Sentences / 542

The Writing Sample / 529

Sample Questions with Answers / 542

Sample Essays / 529

Improving Paragraphs / 546

Important Tips on How to Write the Best Essay / 531

Sample Test with Answers / 548

PA R T 1 0

FIVE SAT PRACTICE TESTS Five Important Reasons for Taking These Practice Tests / 551

551 Explanatory Answers for Practice Test 3 / 815

10 Tips for Taking the Practice Tests / 553

What You Must Do Now to Raise Your SAT Score / 849

Answer Sheet for Practice Test 1 / 555


SAT Practice Test 1 / 561


How Did You Do on This Test? / 607




Raw-Score/Scaled Score Conversion Tables / 613


Chart for Self-Appraisal Based on the Practice Test You Have Just Taken / 616


Explanatory Answers for Practice Test 1 / 619





















SAT Practice Test 3 / 756 How Did You Do on This Test? / 803 Answer Key for Practice Test 3 / 804 Raw-Score/Scaled Score Conversion Tables / 809 Chart for Self-Appraisal Based on the Practice Test You Have Just Taken / 812

Appendices Appendix A: Hot Prefixes and Roots / 1046 Appendix B: Words Commonly Mistaken for Each Other / 1050

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INTRODUCTION I. Important Facts About the SAT

What Is On the SAT? It will include a student-written essay and a multiple-choice writing section testing student’s ability to identify sentence errors, improve sentences, and improve paragraphs. Although grammar and usage will be tested, students will not be asked to define or use grammatical terms, and spelling and capitalization will not be tested. This essay section will be the first part of the test. The Math section will include arithmetic, geometry, algebra I, and some advanced math covering topics in Algebra II, statistics, probability, and data analysis. The test will measure reasoning ability and problem-solving skills. The other parts of the test will contain some long and shorter reading passages, a long paired passage, a short paired passage, and sentence completion questions.

How Will the Test Be Scored? There will be a range of three scores each from 200–800 for the Writing, Math, and Critical Reading.

How Long Will the Test Be? The total time of the test will be 3 hours and 45 minutes.

What Verbal Background Must I Have? The reading and vocabulary level is at the 10th- to 12th-grade level, but strategies presented in this book will help you even if you are at a lower grade level.

What Math Background Must I Have? The Math part will test first- and second-year algebra (Algebra I and II) and geometry. However, if you use common sense and rely on just a handful of geometrical formulas and learn the strategies and thinking skills presented in this book, you don’t need to take a full course in geometry or memorize all the theorems. If you have not taken algebra, you should still be able to answer many of the math questions using the strategies presented in this book.

xiii

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xiv • INTRODUCTION

Is Guessing Still Advisable? Although there is a small penalty for wrong answers (1/4 point for 5-choice questions), in the long run, you break even if you guess or leave the answer blank. For a full explanation of why, see p. 61, Strategy 3. So it really will not affect your score in the long run if you guess or leave answers out. And, if you can eliminate an incorrect choice, it is imperative that you do not leave the answer blank.

Can I Use a Calculator on the Math Portion of the Test? Students can use a four-function, scientific, or graphing calculator. While it is possible to solve every question without the use of a calculator, it is recommended that you use a calculator if you don’t immediately see a faster way to solve the problem without a calculator.

Should I Take an Administered Actual SAT for Practice? Yes, but only if you will learn from your mistakes by seeing what strategies you should have used on your exam. Taking the SAT merely for its own sake is a waste of time and may in fact reinforce bad methods and habits. Note that the SAT is released to students on their Question and Answer Service three times a year, usually in the January, May, and October administrations. It is wise to take exams on these dates if you wish to see your mistakes and correct them.

A Table of What’s on the SAT Math Time

70 min. (Two 25 min. sections, One 20 min. section)

Content

Multiple-Choice Items Student-Produced Responses Measuring: Number and Operations Algebra I, II, and Functions Geometry, Statistics, Probability, and Data Analysis

Score

M 200–800

Critical Reading Time

70 min. (Two 25 min. sections, One 20 min. section)

Content

Sentence Completion Critical Reading: Short and Long Reading Passages with one Double Long Passage and one Double Short Passage

Score

CR 200–800

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INTRODUCTION • xv

Writing Time

60 min. (25 min. essay, 35 min. multiple-choice in two sections)

Content

Multiple-Choice: Identifying Errors Improving Sentences and Paragraphs and Student-Written Essay; Effectively Communicate a Viewpoint, Defining and Supporting a Position

Score

W 200–800 Essay Subscore: 2–12 Multiple-Choice Subscore: 20–80

Note: There is an experimental section that does not count toward your SAT score. This section can contain any of the SAT item types (writing [multiple-choice], critical reading, or math) and can appear in any part of the test. Do not try to outguess the test maker by trying to figure out which of the sections are experimental on the actual test (believe me, you won’t be able to)—treat every section as if it counts toward your SAT score.

A Table of What’s on the PSAT Math Time

50 min. (Two 25 min. sections)

Content

Multiple-Choice Items Student-Produced Responses Measuring: Number and Operations Algebra I and Functions Geometry and Measurement; Statistics, Probability, and Data Analysis

Score

20–80

Critical Reading Time

50 min. (Two 25 min. sections)

Content

Sentence Completion Critical Reading: Short and Long Reading Passages, with one Double Long Passage and one Double Short Passage

Score

20–80

Writing Time

30 min. (one section)

Content

Multiple-Choice: Identifying Errors Improving Sentences and Paragraphs Measuring: Grammar, Usage, Word Choice

Score

20–80

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xvi • INTRODUCTION

Can I Get Back the SAT with My Answers and the Correct Ones After I Take It? How Can I Make Use of This Service? The SAT is disclosed (sent back to the student on request with a $16.00 payment) 3 of the 7 times it is given through the year. Very few people take advantage of this fact or use the disclosed SAT to see what mistakes they’ve made and what strategies they could have used on the questions. Check in your SAT information bulletin or log on to www.collegeboard.com for the dates this Question and Answer Service is available.

Should I Use Scrap Paper to Write on and to Do Calculations? Always use your test booklet (not your answer sheet) to draw on. Many of my strategies expect you to label diagrams, draw and extend lines, circle important words and sentences, etc., so feel free to write anything in your booklet. The booklets aren’t graded—just the answer sheets (see General Strategy 4, page 61).

Should I Be Familiar with the Directions to the Various Items on the SAT Before Taking the SAT? Make sure you are completely familiar with the directions to each of the item types on the SAT—the directions for answering the Sentence Completions, the Reading, the Regular Math, and especially the Grid-Type (see General Strategy 2, page 60).

What Should a Student Bring to the Exam on the Test Date? You should bring a few sharpened #2 pencils with erasers, and also your ID. Bring a calculator to the test, but be aware that every math question on the SAT can be solved without a calculator; in many questions, it’s actually easier not to use one. Acceptable calculators: Graphing calculators, scientific calculators, and four-function calculators (the last is not recommended) are all permitted during testing. If you have a calculator with characters that are one inch or higher, or if your calculator has a raised display that might be visible to other test takers, you will be seated at the discretion of the test supervisor. Unacceptable calculators: Laptops or portable/handheld computers; calculators that have a QWERTY keyboard, make noise, use an electrical outlet, or have a paper tape; electronic writing pads or stylus-driven devices; pocket organizers; and cell phone calculators will not be allowed during the test.

How Should a Student Pace Himself/Herself on the Exam? How Much Time Should One Spend on Each Question? Calculate the time allowed for the particular section. For example, 25 minutes. Divide by the number of questions. For example, 20. That gives you an average of spending 11⁄4 minutes per question in this example. However, the first set of questions within an item type in a section are easier, so spend less than a minute on the first set of questions and perhaps more than a minute on the last set. With the reading passages you should give yourself only about 30 seconds a question and spend the extra time on the reading passages. Also, more difficult reading questions may take more time.

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INTRODUCTION • xvii

How Is the Exam Scored? Are Some Questions Worth More Points? Each question is worth the same number of points. After getting a raw score—the number of questions right minus a penalty for wrong answers—this is equated to a “scaled” score from 200 to 800 in each of the Critical Reading, Math, and Writing sections. A scaled score of 500 in each part is considered “average.”

It’s 3 Days Until the SAT; What Can a Student Do to Prepare? Make sure you are completely familiar with the structure of the test (page xxii), the basic math skills needed (pages 155–164), and the basic verbal skills, such as prefixes and roots (pages 352–356). Take a few practice tests and refresh your understanding of the strategies used to answer the questions (see page xxiii for the Four-Hour Study Program).

What Is the Most Challenging Type of Question on the Exam and How Does One Attack It? Many questions, especially at the end of a section, on the test can be challenging. You should always attack challenging questions by using a specific strategy or strategies and common sense.

What Should a Student Do to Prepare on Friday Night? Cram? Watch TV? Relax? On Friday night, I would just refresh my knowledge of the structure of the test, some strategies, and refresh some basic skills (verbal or math). You want to do this to keep the thinking going so that it is continual right up to the exam. Don’t overdo it, just enough so that it’s somewhat continuous—this will also relieve some anxiety, so that you won’t feel you are forgetting things before the exam.

The Test Is Given in One Booklet. Can a Student Skip Between Sections? No-—you cannot skip between the sections. You have to work on the section until the time is called. If you get caught skipping sections or going back to earlier sections, then you risk being asked to leave the exam.

Should a Student Answer All Easy Questions First and Save Difficult Ones for Last? The easy questions usually appear at the beginning of the section, the middle difficulty ones in the middle, and the hard ones toward the end. So I would answer the questions as they are presented to you, and if you find you are spending more than 30 seconds on a question and not getting anywhere, go to the next question. You may, however, find that the more difficult questions toward the end are actually easy for you because you have learned the strategies in this book.

What Is the Recommended Course of Study for Those Retaking the Exam? Try to get a copy of the exam that you took if it was a disclosed one—the disclosed ones, which you have to send a payment for, are usually given in October, January, and May. Try to learn from your mistakes by seeing what strategies you could have used to get questions right. Certainly learn the specific strategies for taking your next exam.

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What Are the Most Crucial Strategies for Students? All specific Verbal (Critical Reading) and Math Strategies are crucial, including the general test-taking strategies (described on pages 60–153), guessing, writing and drawing in your test booklet, and being familiar with question-type directions. The key Reading Strategy is to know the four general types of questions that are asked in reading—main idea, inference, specific details, and tone or mood. In math, it’s the translations strategy—verbal to math, drawing of lines, etc. Also make sure you know the math basic skills cold (see pages 155–164 for these rules—make sure you know them).

I Know There Is an Experimental Section on the Exam That Is Not Scored. How Do I Know Which Section It Is? The SAT people have now made it so difficult to tell which is the experimental section, I would not take a chance second-guessing them and leaving it out. It will look like any of the other sections. It is true that if you have, for example, two of the same sections, such as two sections that both deal with grid questions, one of them is experimental—but you won’t know which one it is. Also, if you have two sections where there is a long double reading passage, one of those sections is experimental, but again you won’t know which one it is.

Can I Take the Test More Than Once, and If So, How Will the Scores Be Reported to the Schools of My Choice? Will All Scores Be Reported to the School and How Will They Be Used? Check with the schools you are applying to to see how they use the reported scores, e.g., whether they average them, whether they take the highest. Ask the schools whether they see unreported scores; if they do, find out how the individual school deals with single and multiple unreported scores.

How Do Other Exams Compare with the SAT? Can I Use the Strategies and Examples in This Book for Them? Most other exams are modeled after the SAT, and so the strategies used here are definitely useful when taking them. For example, the GRE (Graduate Records Examination, for entrance into graduate school) has questions that use the identical strategies used on the SAT. The questions are just worded at a slightly higher level. The ACT (American College Testing Program), another college entrance exam, reflects more than ever strategies that are used on the SAT.

How Does the Gruber Preparation Method Differ from Other Programs and SAT Books? Many other SAT programs try to use “quick fix” methods or subscribe to memorization. Socalled “quick fix” methods can be detrimental to effective preparation because the SAT people constantly change questions to prevent “gimmick” approaches. Rote memorization methods do not enable you to answer a variety of questions that appear in the SAT exam. In more than

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thirty years of experience writing preparation books for the SAT, Dr. Gruber has developed and honed the Critical Thinking Skills and Strategies that are based on all standardized tests’ construction. So, while his method immediately improves your per formance on the SAT, it also provides you with the confidence to tackle problems in all areas of study for the rest of your life. He remarkably enables you to be able to, without panic, look at a problem or question, extract something curious or useful from the problem, and lead you to the next step and finally to a solution, without rushing into a wrong answer or getting lured into a wrong choice. It has been said that test taking through his methodology becomes enjoyable rather than a pain.

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xx • INTRODUCTION

II. The Inside Track on How SAT Questions Are Developed and How They Vary from Test to Test When an SAT question is developed, it is based on a set of criteria and guidelines. Knowing how these guidelines work should demystify the test-making process and convince you why the strategies in this book are so critical to getting a high score. Inherent in the SAT questions are Critical Thinking Skills, which present strategies that enable you to solve a question by the quickest method with the least amount of panic and brain-racking and describe an elegance and excitement in problem solving. Adhering to and using the strategies (which the test makers use to develop the questions) will let you “sail” through the SAT. This is summed up in the following statement: Show me the solution to a problem, and I’ll solve that problem. Show me a Gruber strategy for solving the problem, and I’ll solve hundreds of problems. —Gary Gruber

Here’s a sample of a set of guidelines presented for making up an SAT-type question in the Math area: The test maker is to make up a hard math problem in either the regular math multiple-choice area or the quantitative comparison area which involves (A) algebra (B) two or more equations (C) two or more ways to solve: one way being standard substitution, the other faster way using the strategy of merely adding or subtracting equations.*

Previous examples given to test maker for reference: 1. If x y 3, y z 4 and z x 5, find the value of

x y z. (A) 4 (B) 5 (C) 6 (D) 7 (E) 8

Solution: Add equations and get 2x 2y 2z 12; divide both sides of the equation by 2 and we get x y z 6. (Answer C) 2. If 2x y 8 and x 2y 4, find the value of x y.

(A) 3 (B) 4 (C) 5 (D) 6 (E) 7 Solution: Subtract equations and get x y 4. (Answer B) Here’s an example from a recent SAT. If y x 5 and 2y z 11, find the value of x y z. (A) 3 (B) 6 (C) 8 (D) 16 (E) 55 Solution: Subtract equation y x 5 from 2y z 11. We get 2y y z ( x) 11 5. So, y z x 6. (Choice B)

* Note: See Math Strategy #13 on p. 100.

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III. What Are Critical Thinking Skills? Critical Thinking Skills, a buzz phrase now in the nation, are generic skills for the creative and most effective way of solving a problem or evaluating a situation. The most effective way of solving a problem is to extract some piece of information or observe something curious from the problem then use one or more of the specific strategies or Critical Thinking Skills (together with basic skills or information you already know) to get to the next step in the problem. This next step will catapult you toward a solution with further use of the specific strategies or thinking skills. 1. EXTRACT OR OBSERVE SOMETHING CURIOUS 2. USE SPECIFIC STRATEGIES TOGETHER WITH BASIC SKILLS These specific strategies will enable you to “process” think rather than just be concerned with the end result, the latter which usually gets you into a fast, rushed, and wrong answer. The Gruber strategies have been shown to make one more comfortable with problem solving and make the process enjoyable. The skills will last a lifetime, and you will develop a passion for problem solving. These Critical Thinking Skills show that conventional “drill and practice” is a waste of time unless the practice is based on these generic thinking skills.

Here’s a simple example of how these Critical Thinking Skills can be used in a math problem: 1 1 1 1 1 Which is greater, 7 8 6 or 8 6 7? 7 8 6 8 6 1 1 1 1 1 Long and tedious way: Multiply 7 8 6 and compare it with 8 6 7. 7 8 6 8 6

Error in doing the problem the “long way”: You don’t have to calculate; you just have to compare, so you need a strategy for comparing two quantities. 1 1 Critical Thinking Way: 1. Observe: There is a common 8 and 6 8 6 1 1 2. Use Strategy: Since both 8 and 6 are just weighting factors, like 8 6 the same quantities on both sides of a balance scale, just cancel them from both multiplied quantities above. 1 1 3. You are then left comparing 7 with 7, so the first quantity, 7 , is 7 7 1 1 1 1 1 greater. Thus 7 8 6 is greater than 8 6 7. 7 8 6 8 6

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Here’s a simple example of how Critical Thinking Skills can be used for a Verbal problem: If you see a word such as DELUDE in a sentence or in a reading passage, you can assume that the word DELUDE is negative and probably means “taking away from something” or “distracting,” since the prefix DE means “away from” and thus has a negative connotation. Although you may not get the exact meaning of the word (in this case the meaning is to “deceive” or “mislead”), you can see how the word may be used in the context of the sentence it appears in, and thus get the flavor or feeling of the sentence, paragraph, or sentence completion. I have researched and developed more than 50 prefixes and roots (present in this book) that can let you make use of this context strategy. Notice that the Critical Thinking approach gives you a fail-safe and exact way to the solution without superficially trying to solve the problem or merely guessing at it. This book contains all the Critical Thinking Strategies you need to know for the SAT test. Dr. Gruber has researched hundreds of SAT tests (thousands of SAT questions) and documented 40 Critical Thinking Strategies (all found in this book) coursing through ever y test. These strategies can be used for any Math, Verbal, or Logical Reasoning problem. In short, you can learn how to solve a specific problem and thus find how to answer that specific problem, or you can learn a powerful strategy that will enable you to answer hundreds of problems.

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IV. Strategies for Women

These are questions that women found significantly more difficult than men. However, after learning the strategies in this book, women scored just as high as men on these sections.

Verbal Sentence Completion

Math 1. Carol has twice as many books as Beverly has. After

Carol gives Beverly 5 books, she still has 10 more books than Beverly has. How many books did Carol have originally?

Choose the word or set of words that when inserted in the sentence best fits the meaning of the sentence as a whole.

(A) 20

1. The most ____ means of transportation in the

world is the bicycle; indeed, no powered vehicle requires less energy to move as much mass over the same distance. (A) (B) (C) (D) (E)

grandiose infallible efficient engrossing unstable

2. The artistry of cellist Yo Yo Ma is essentially____;

the melodic line rises____, imbued with feeling and totally lacking in apparent calculation. (A) carefree / stiffly (B) reserved / involuntarily (C) lyrical / passionately (D) detached / carefully (E) deliberate / methodically

(B) 25

(C) 30

(D) 35

(E) 40

5 2 X 9 5, 2 ▫ 8

2.

In the correctly computed multiplication problem above, if and □ are different digits, then

(A) 1

(B) 5

(C) 6

(D) 7

(E) 8

3. If s equals 1/2 percent of t, what percent of s is t?

(A) 2% (B) 200% (C) 2,000% (D) 20,000% (E) 200,000%

Answers, Strategy, and Page in Book for Questions: ANSWER

STRATEGY

Verbal 1. C 2. C

Sentence Completion 1 Sentence Completion 2, 4

Math 1. E 2. E 3. D

Math 2 Math 8 Math 2 and 7

PAGE 245 246, 249

176 193 176, 191

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V. Multi-Level Approaches to Solution of Problems How a student answers a question is more important than the answer given by the student. For example, the student may have randomly guessed, the student may have used a rote and unimaginative method for solution, or the student may have used a very creative method. It seems that one should judge the student by the “way” he or she answers the question and not just by the answer to the question. Example: Question: Without using a calculator, which is greater: 355 ⴛ 356 or 354 ⴛ 357? Case 1: Rote Memory Approach (a completely mechanical approach not realizing the fact that there may be a faster method that takes into account patterns or connections of the numbers in the question): The student multiplies 355 356, gets 126,380 and then multiplies 354 357 and gets 126,378. Case 2: Obser ver’s Rote Approach (an approach which makes use of a mathematical strategy that can be memorized and tried for various problems): The student does the following: Divide both quantities by 354: He or she then gets 355 356/354 compared with 354 357/354. He or she then divides these quantities by 356 and then gets 355/354 compared with 357/356. Now he or she realizes that 355/354 1 and 1/354; 357/356 1 and 1/356. He or she then reasons that since the left side 1 and 1/354 is greater than the right side, 1 and 1/356, the left side of the original quantities, 355 356, is greater than the right side of the original quantities 354 357. Case 3: The Pattern Seeker’s Method (most mathematically creative method—an approach in which the student looks for a pattern or sequence in the numbers and then is astute enough to represent the pattern or sequence in more general algebraic language to see the pattern or sequence more clearly): Look for a pattern. Represent 355 356 and 354 357 by symbols. Let x 354. Then 355 x 1, 356 x 2, 357 x 3. So 355 356 (x 1) (x 2) and 354 357 x(x 3). Multiplying the factors we get 355 356 (x times x) 3x 2 and 354 357 (x times x) 3x. The difference: 355 356 354 357 (x times x) 3x 2 minus (x times x) minus 3x, which is just 2. So 355 356 is greater than 354 357 by 2. Note: You could have also represented 355 by x. Then 356 x 1; 354 x 1; 357 x 2. We would then get 355 356 (x)(x 1) and 354 357 (x 1)(x 2). Then we would use the method above to compare the quantities. —OR— You could have written 354 as a and 357 as b. Then 355 a 1 and 356 b 1. So 355 356 (a 1) (b 1) and 354 357 ab. Let’s see what (355 356) (354 357) is. This is the same as (a 1) (b 1) ab, which is (ab b a 1) ab, which is in turn b a 1. Since b a 1 357 354 1 2, the quantity 355 356 354 357 2, so 355 356 is is greater than 354 357 by 2.

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Case 4: The Astute Obser ver’s Approach (simplest approach—an approach which attempts to figure out a connection between the numbers and uses that connection to figure out the solution): 355 356 (354 1) 356 (354 356) 356 and 354 357 354 (356 1) (354 356) 354 One can see that the difference is just 2. Case 5: The Observer’s Common Relation Approach (this is the approach that people use when they want to connect two items to a third to see how the two items are related): 355 356 is greater than 354 356 by 356. 354 357 is greater than 354 356 by 354. So this means that 355 356 is greater than 354 357. Case 6: Scientific, Creative and Observational Generalization Method (a highly creative method and the most scientific method, as it spots a critical and curious aspect of the sums being equal and provides for a generalization to other problems of that nature): Represent 354 a, 357 b, 355 c, and 356 d We have now that (1) a b c d (2) b a d c We want to prove: ab < dc Proof: Square inequality (2): (b a)2 > (d c)2 Therefore: (3) b2 2ab a2 > d2 2dc c2 Multiply (3) by (1) and this reverses the inequality sign: (b2 2ab a2) < (d2 2dc c2) or (4) b2 2ab a2 < d2 2dc c2 Now square (1): (a b) (c d) and we get: (5) a2 2ab b2 c2 2dc d2 Add inequality (4) to equality (5) and we get: 4ab < 4dc Divide by 4 and we get: ab < dc The generalization is that for any positive numbers a,b,c,d when b a > d c and a b c d, then ab < dc. This also generalizes in a geometrical setting where for two rectangles whose perimeters are the same (2a 2b 2c 2d), the rectangle whose absolute difference in sides d c is least has the greatest area. Case 7: Geometric and Visual Approach*: (this is the approach used by visual people or people that have a curious geometric bent and possess “out-of-the-box” insights): d b

c a

Where a 354, b 357, c 355, and d 356, we have two rectangles where the first one’s length is d and width is c, and the second one’s length is b (dotted line) and width is a. Now the area of the first rectangle (dc) is equal to the area of the second (ab) minus the area of the rectangular slab which is (b d)a plus the area of the rectangular slab (c a)d. So we get: cd ab (b d)a (c a)d. Since b d c a, we get cd ab (c a)a (c a)d ab (d a)(c a). Since d > a and c > a, cd > ab. So 355 356 > 354 357.

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*This method of solution was developed by and sent to the author from Dr. Eric Cornell, a Nobel Laureate in Physics.

-----------------------------------------------------------------------------Note: Many people have thought that by multiplying units digits from one quantity and comparing that with the multiplication of the units digits from the other quantity that they’d get the answer. For example, they would multiply 5 6 30 from 355 356 then multiply 4 7 28 from 354 357 and then say that 355 356 is greater than 354 357 because 5 6 > 4 7. They would be lucky. That works if the sum of units digits of the first quantity is the same as or greater than the sum of units digits of the second quantity. However, if we want to compare something like 354 356 126,024 with 352 359 126,368, that initial method would not work.

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VI. A Four-Hour Study Program for the SAT For those who have only a few hours to spend in SAT preparation, I have worked a minimum study program to get you by. It tells you what basic Math skills you need to know, what vocabulary practice you need, and the most important strategies you need from the 40 in this book.

General Study General Strategies, pages 60–61.

Critical Reading Study the following Verbal Strategies beginning on page 118 (first 3 questions): Sentence Completion Strategies 1, 2, pages 118–120 Vocabulary Strategies 1, 2, and 3, pages 148–153 Reading Comprehension Strategies 1 and 2, pages 133–137 Study the 291 Most Important/Frequently Used SAT Words and Their Opposites, page 359.

Math Study the Mini-Math Refresher beginning on page 155. Study the following Math Strategies beginning on page 69* (first 3 questions for each strategy):

Strategy 2, page 71 Strategy 4, page 80 Strategy 8, page 90 Strategy 12, page 98 Strategy 13, page 100 Strategy 14, page 102 Strategy 17, page 109 Strategy 18, page 112

If you have time, take Practice Test 1 starting on page 554. Do sections 1–10. Check your answers with the explanatory answers starting on page 618, and look again at the strategies and basic skills that apply to the questions you missed.

Writing Look through the material in Part 9—The SAT Writing Test starting on page 523.

*Make sure you read pages 62–68 before you study Math Strategies.

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VII. Longer-Range Study Program and Helpful Steps for Using This Book 1. Learn the 5 General Strategies for test taking on pages 60–61. 2. Take the Strategy Diagnostic SAT test on page 1 and follow the directions for diagnosis in (3).

3. Take the SAT Test 1 on page 554 and score yourself according to the instructions.

4. For those problems or questions that you answered incorrectly or were uncertain of, see the explanatory answers, beginning on page 618, and make sure that you learn the strategies keyed to the questions, beginning on page 59. For complete strategy development, it is a good idea to

study all the strategies beginning on page 59, Part 4 of the Strategy section, and learn how to do all the problems within each strategy. 5. If you are weak in basic Math skills, take the 101 Most Important Math Questions Test on page 29 and follow the directions for diagnosis. 6. To see if you are making use of the strategies you’ve learned, you should take the Shortest SAT test and follow the directions for diagnosis. Part 2, page 23.

For Vocabulary Building 7. Learn the special Latin and Greek prefixes, roots, and suffixes beginning on page 352. This will significantly build your vocabulary. You may also want to study the Hot Prefixes and Roots in Appendix A. 8. Study 100 words per day from the 3,400 Word List, page 363.

9. Optional: Take the vocabulary tests beginning on page 415.

10. Study the 291 Most Important/Frequently Used SAT Words and Their Opposites beginning on page 359.

For Math-Area Basic Skills Help 11. For the basic Math skills keyed to the questions, study the SAT Math Refresher beginning on page

165, or for quicker review, look at the Mini-Math Refresher, beginning on page 155.

For Writing Help 12. Look through Part 9—The SAT Writing test beginning on p. 523. You may also wish to refresh

your grammar ability by looking through the Grammar and Usage Refresher starting on p. 461.

Now 13. Take the remaining four Practice SAT tests beginning on page 653, score yourself, and go over your answers with the explanatory answers. Always refer to the associated strategies and

basic skills for questions you answered incorrectly or were not sure how to do.

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VIII. Format of the SAT

Total time for “counted” (not experimental) CRITICAL READING: 70 minutes—67 questions Total time for “counted” (not experimental) MATH: 70 minutes—54 questions Total time for “counted” (not experimental) WRITING (Multiple-Choice): 35 minutes—49 questions Total time for WRITING (Essay): 25 minutes—1 or 2 prompts Total time for experimental, pre-test items: 25 minutes—number of questions varies Note: The following represents a form of an SAT. The SAT has many different forms, so the order of the sections may vary and the experimental section* may not be the third section as we have here. However, the first section will always be the Essay and the last section will be a 10minute Multiple-Choice Writing section. Number of Questions

Number of Minutes

Section 1: WRITING (Essay)

1

25

Section 2: MATH Regular Math

20 20

25

10 Sections of the SAT*

5 minute break Section 3: EXPERIMENTAL* Could be Writing, Critical Reading, or Math

varies

25

Section 4: CRITICAL READING Sentence Completions 1 short passage (60–125 wds) 1 short passage (60–125 wds) 1 passage (650–850 wds) OR Double reading passage (350–450 wds each)

24 8 2 2 11–13

25

11–13 1 minute break

Section 5: WRITING (Multiple-Choice) Improving Sentences Identifying Errors Improving Paragraphs

35

Section 6: MATH Regular Math Student-Produced (“grid type”)

18 8 10

25

11 18 6 25

5 minute break Section 7: CRITICAL READING Sentence Completions 1 paired short passage (about 130 wds each) 1 passage (400–550 wds) 1 passage (550–700 wds)

24 5 4 5–7 8–10

25

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xxx • INTRODUCTION

Number of Questions

Number of Minutes

Section 8: MATH Regular Math

16 16

20

Section 9: CRITICAL READING Sentence Completions Double reading passage (350–450 wds each) OR 1 passage (650–850 wds)

19 6 13

20

Section 10: WRITING (Multiple Choice) Improving Sentences

14 14

10 Sections of the SAT*

13 10

TOTAL MINUTES 225 (3 3/4 hours) *The order of the sections on the actual test varies since the SAT has several different forms. There will be passages on Humanities, Social Sciences, Natural Sciences, and Narrative (fiction or nonfiction). Total number of counted reading questions will be 48. Note: One of the sections is experimental. An experimental section does not count in your SAT score. You cannot tell which of the sections of the test is experimental.

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PA R T 1

STRATEGY DIAGNOSTIC TEST FOR THE SAT Take This Test to Find Out What Strategies You Don’t Know The purpose of this test is to find out how you approach SAT problems of different types and to reveal your understanding and command of the various strategies and Critical Thinking Skills. After checking your answers in the table at the end of the test, you will have a profile of your performance. You will know exactly what strategies you must master and where you may learn them.

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2 • STRATEGY DIAGNOSTIC TEST FOR THE SAT

Directions for Taking the Diagnostic Test

For each odd-numbered question (1, 3, 5, 7, etc.), choose the best answer. In the even-numbered questions (2, 4, 6, 8, etc.), you will be asked how you solved the preceding odd-numbered question. Make sure that you answer the even-numbered questions carefully, as your answers will determine whether or not you used the right strategy. Be completely honest in your answers to the even-numbered questions, since you do want an accurate assessment in order to be helped. EXAMPLE:

1.

The value of 17 98 17 2 (A) 1,550 (B) 1,600 (C) 1,700 (D) 1,800 (E) 1,850 (The correct answer is Choice C.)

2.

How did you get your answer? (A) I multiplied 17 98 and added that to 17 2. (B) I approximated and found the closest match in the choices. (C) I factored 17 to get 17(98 2). (D) I guessed. (E) By none of the above methods.

In question 2: • If you chose A, you did the problem the long way unless you used a calculator.

• If you chose B, you probably approximated 98 by 100 and got 1,700. • If you chose C, you factored out the 17 to get 17(98 2) 17(100) 1,700. This was the best strategy to use. • If you chose D, you probably didn’t know how to solve the problem and just guessed. • If you chose E, you did not use any of the methods above but used your own different method. Note: In the even-numbered questions, you may have used a different approach from what will be described in the answer to that question. It is, however, a good idea to see if the alternate approach is described, as you may want to use that approach for solving other questions. Now turn to the next page to take the test.

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STRATEGY DIAGNOSTIC TEST FOR THE SAT • 3

Strategy Diagnostic Test Answer Sheet

SECTION

1 Verbal Ability

SECTION

2 Math Ability

1 2 3 4 5 6 7 8 9 10 11 12 13 14

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

1 2 3 4 5 6 7 8 9

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

15 16 17 18 19 20 21 22 23 24 25 26 27 28

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

10 11 12 13 14 15 16 17 18

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

29 30 31 32 33 34 35 36 37 38 39 40 41 42

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

19 20 21 22 23 24 25 26 27

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

43 44 45 46 47 48 49 50 51 52 53 54 55 56

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

28 29 30 31 32 33 34 35 36

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

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Section 1: Verbal Ability

Each of the following sentences has one or two blanks, each blank indicating that something has been omitted. Beneath the sentence are five lettered words or sets of words. Choose the word or set of words that best fits the meaning of the sentence as a whole. EXAMPLE:

Although its publicity has been ————, the film itself is intelligent, well-acted, handsomely produced, and altogether ————. (A) (B) (C) (D) (E)

tasteless . . . respectable extensive . . . moderate sophisticated . . . amateur risqué . . . crude perfect . . . spectacular A

1.

C

D

E

He believed that while there is serious unemployment in our auto industry, we should not ———— foreign cars. (A) (B) (C) (D) (E)

2.

B

3.

build repair review import consolidate

The salesmen in that clothing store are so ——— that it is impossible to even look at a garment without being ——— by their efforts to convince you to purchase. (A) (B) (C) (D) (E)

offensive . . . considerate persistent . . . irritated extensive . . . induced immune . . . aided intriguing . . . evaluated

How did you get your answer? (A) I tried the word from each choice in the blank and came up with the best answer. (B) I chose a word from the choices that “sounded good” but that I am really not sure is correct. (C) I tried to figure out, before looking at the choices, what word would fit into the blank. Then I matched that word with the choices. (D) I guessed. (E) None of these.

4.

How did you get your answer? (A) I tried each choice (two words at a time) in the blanks to see which made for the best sentence. (B) I tried to see what words I could come up with for the blanks before looking at the choices. (C) I tried the first word from each of the choices in the first blank in the sentence to see which made the most sense. Then I eliminated the choices whose first words didn’t make sense in the sentence. Finally, I tried both words in the remaining choices to further eliminate incorrect choices. (D) I guessed. (E) None of these.

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5.

Many buildings with historical significance are now being ——— instead of being torn down. (A) (B) (C) (D) (E)

6.

How did you get your answer?

a successful a delightful a headstrong an understanding a solitary

How did you get your answer? (A) I tried all the choices in the sentence and selected the best one. (B) I realized, from the word Being and from the phrase after the comma, that there was a connection between the two parts of the sentence. (C) I looked for the most difficult-sounding word. (D) I guessed. (E) None of these.

9.

11.

Being ——— person, he insisted at the conference that when he spoke he was not to be interrupted. (A) (B) (C) (D) (E)

8.

(A) I tried both words from each choice in the blanks to see which choice made the sentence sound best. (B) I tried the first word from each choice in the first blank of the sentence to eliminate choices. Then I tried both words from the remaining choices to further eliminate choices. (C) I realized that the words in spite of would create an opposition or contrast between the two parts of the sentence and therefore looked for words in the choices that were opposites. (D) I guessed. (E) None of these.

built forgotten destroyed praised repaired

(A) I tried each of the choices in the blank. (B) I tried to find my own word that would fit the blank before looking at the choices. Then I matched one of the choices with my word. (C) I looked for a word that meant the opposite of “being torn down.” (D) I guessed. (E) None of these. 7.

10. How did you get your answer?

In spite of the ——— of her presentation, many people were ——— with the speaker’s concepts and ideas. (A) interest . . . enthralled (B) power . . . taken (C) intensity . . . shocked (D) greatness . . . gratified (E) strength . . . bored

Richard Wagner was frequently intolerant; moreover, his strange behavior caused most of his acquaintances to _______ the composer whenever possible. (A) (B) (C) (D) (E)

12.

contradict interrogate shun revere tolerate

How did you get your answer? (A) I tried all the choices in the blank and selected the best one. (B) I realized that the word moreover indicated support so I looked for a choice that would represent a support of what was in the first part of the sentence. (C) I tried to find my own word to fit the blank. Then I matched that word with a word in one of the choices. (D) I guessed. (E) None of these.

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Each of the following questions consists of a word in capital letters, followed by five lettered words or phrases. Choose the word or phrase that is most nearly opposite in meaning to the word in capital letters. Since some of the questions require you to distinguish fine shades of meaning, consider all the choices before deciding which is best. EXAMPLE:

GOOD: (A) sour (B) bad (C) red (D) hot (E) ugly A

C

D

E

Note: Although Antonyms is no longer a part of the SAT, we are still testing vocabulary through antonyms on this particular test, since it is still important for you to develop vocabulary strategies for the Sentence Completions and Reading Comprehension parts of the SAT. 13.

changing stupid unconscious poor antagonistic

15.

antiseptic unwilling inconsiderate retarded awkward

How did you get your answer? (A) I knew what the prefix PRO meant and used it to figure out the capitalized word, but I didn’t use any root of PROFICIENT. (B) I used the meaning of the prefix PRO and the meaning of the root FIC to figure out the meaning of the word PROFICIENT. (C) I knew from memory what the word PROFICIENT meant. (D) I guessed. (E) None of these.

include guide reply upgrade welcome

How did you get your answer? (A) I knew what the prefix DE meant and used it to figure out the meaning of the word DELUDE, but I didn’t use any root of DELUDE. (B) I used the meaning of the prefix DE and the meaning of the root LUD to figure out the meaning of the word DELUDE. (C) I knew from memory what the word DELUDE meant. (D) I guessed. (E) None of these.

19.

POTENT: (A) (B) (C) (D) (E)

PROFICIENT: (A) (B) (C) (D) (E)

16.

18.

How did you get your answer? (A) I knew the meaning of the word TENACIOUS. (B) I knew what the root TEN meant and looked for the opposite of that root. (C) I did not know what TENACIOUS meant but knew a word that sounded like TENACIOUS. (D) I guessed. (E) None of these.

DELUDE: (A) (B) (C) (D) (E)

TENACIOUS: (A) (B) (C) (D) (E)

14.

17.

20.

imposing pertinent feeble comparable frantic

How did you get your answer? (A) I knew what the CAPITALIZED word meant. (B) I knew a word or part of a word that sounded the same as POTENT or had a close association with the word POTENT. (C) I knew a prefix or root of the CAPITALIZED word, which gave me a clue to the meaning of the word. (D) I knew from a part of the CAPITALIZED word that the word had a negative or positive association. Thus, I selected a choice that was opposite in flavor (positive or negative). (E) None of these.

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21.

RECEDE: (A) (B) (C) (D) (E)

22.

accede settle surrender advance reform

27.

28.

24.

improving possible beginning reduced frigid

25.

SLOTHFUL: (A) (B) (C) (D) (E)

permanent ambitious average truthful plentiful

disloyalty stinginess dispersion simplicity vehemence

How did you get your answer? (A) I knew what the CAPITALIZED word meant. (B) I knew a word or part of a word that sounded the same as MUNIFICENCE or had a close association with the word MUNIFICENCE. (C) I knew a prefix or root of the CAPITALIZED word, which gave me a clue to the meaning of the word. (D) I knew from a part of the CAPITALIZED word that the word had a negative or positive association. Thus, I selected a choice that was opposite in flavor (positive or negative). (E) None of these.

How did you get your answer? (A) I knew what the CAPITALIZED word meant. (B) I knew a word or part of a word that sounded the same as THERMAL or had a close association with the word THERMAL. (C) I knew a prefix or root of the CAPITALIZED word, which gave me a clue to the meaning of the word. (D) I knew from a part of the CAPITALIZED word that the word had a negative or positive association. Thus, I selected a choice that was opposite in flavor (positive or negative). (E) None of these.

MUNIFICENCE: (A) (B) (C) (D) (E)

THERMAL: (A) (B) (C) (D) (E)

How did you get your answer? (A) I knew what the CAPITALIZED word meant. (B) I knew a word or part of a word that sounded the same as SLOTH or had a close association with the word SLOTH. (C) I knew a prefix or root of the CAPITALIZED word, which gave me a clue to the meaning of the word. (D) I knew from a part of the CAPITALIZED word that the word had a negative or positive association. Thus, I selected a choice that was opposite in flavor (positive or negative). (E) None of these.

How did you get your answer? (A) I found a word opposite in meaning to the word RECEDE, without looking at the choices. Then I matched my word with the choices. (B) I used prefixes and/or roots to get the meaning of the word RECEDE. (C) I looked at the choices to see which word was opposite to RECEDE. I did not try first to get my own word that was opposite to the meaning of RECEDE, as in Choice A. (D) I guessed. (E) None of these.

23.

26.

29.

FORTITUDE: (A) (B) (C) (D) (E)

30.

timidity conservatism placidity laxness ambition

How did you get your answer? (A) I knew what the CAPITALIZED word meant. (B) I knew a word or part of a word that sounded the same as FORTITUDE or had a close association with the word FORTITUDE. (C) I knew a prefix or root of the CAPITALIZED word, which gave me a clue to the meaning of the word. (D) I knew from a part of the CAPITALIZED word that the word had a negative or positive association. Thus, I selected a choice that was opposite in flavor (positive or negative). (E) None of these.

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31.

DETRIMENT: (A) (B) (C) (D) (E)

32.

recurrence disclosure resemblance enhancement postponement

How did you get your answer? (A) I knew what the CAPITALIZED word meant. (B) I knew a word or part of a word that sounded the same as DETRIMENT or had a close association with the word DETRIMENT. (C) I knew a prefix or root of the CAPITALIZED word, which gave me a clue to the meaning of the word. (D) I knew from a part of the CAPITALIZED word that the word had a negative or positive association. Thus, I selected a choice that was opposite in flavor (positive or negative). (E) None of these.

33.

CIRCUMSPECT: (A) (B) (C) (D) (E)

34.

35.

suspicious overbearing listless determined careless

How did you get your answer? (A) I knew what the CAPITALIZED word meant. (B) I knew a word or part of a word that sounded the same as CIRCUMSPECT or had a close association with the word CIRCUMSPECT. (C) I knew a prefix or root of the CAPITALIZED word, which gave me a clue to the meaning of the word. (D) I knew from a part of the CAPITALIZED word that the word had a negative or positive association. Thus, I selected a choice that was opposite in flavor (positive or negative). (E) None of these.

LUCID: (A) (B) (C) (D) (E)

36.

underlying complex luxurious tight general

How did you get your answer? (A) I knew what the CAPITALIZED word meant. (B) I knew a word or part of a word that sounded the same as LUCID or had a close association with the word LUCID. (C) I knew a prefix or root of the CAPITALIZED word, which gave me a clue to the meaning of the word. (D) I knew from a part of the CAPITALIZED word that the word had a negative or positive association. Thus, I selected a choice that was opposite in flavor (positive or negative). (E) None of these.

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Each of the following passages is followed by questions based on its content. Answer all questions following a passage on the basis of what is stated or implied in that passage.

5

10

15

20

25

30

She walked along the river until a policeman stopped her. It was one o’clock, he said. Not the best time to be walking alone by the side of a half-frozen river. He smiled at her, then offered to walk her home. It was the first day of the new year, 1946, eight and a half months after the British tanks had rumbled into Bergen-Belsen. That February, my mother turned twenty-six. It was difficult for strangers to believe that she had ever been a concentration camp inmate. Her face was smooth and round. She wore lipstick and applied mascara to her large dark eyes. She dressed fashionably. But when she looked into the mirror in the mornings before leaving for work, my mother saw a shell, a mannequin who moved and spoke but who bore only a superficial resemblance to her real self. The people closest to her had vanished. She had no proof that they were truly dead. No eyewitnesses had survived to vouch for her husband’s death. There was no one living who had seen her parents die. The lack of confirmation haunted her. At night before she went to sleep and during the day as she stood pinning dresses she wondered if, by some chance, her parents had gotten past the Germans or had crawled out of the mass grave into which they had been shot and were living, old and helpless, somewhere in Poland. What if only one of them had died? What if they had survived and had died of cold or hunger after she had been liberated, while she was in Celle* dancing with British officers? She did not talk to anyone about these things. No one, she thought, wanted to hear them. She woke up in the morning, went to work, bought groceries, went to the Jewish Community Center and to the housing office like a robot.

39.

(A) (B) (C) (D) (E) 40.

The policeman stopped the author’s mother from walking along the river because (A) (B) (C) (D) (E)

38.

the river was dangerous it was the wrong time of day it was still wartime it was too cold she looked suspicious

Which part of the passage gives you the best clue for getting the right answer? (A) Lines 12: “It was one o’clock, he said.” (B) Lines 13: “It was one o’clock, he said. Not the best time to be walking alone.” (C) Lines 14: “It was one o’clock, he said. Not the best time to be walking alone by the side of a half-frozen river.” (D) None of these. (E) I don’t know.

walked along the river thought about death danced with the officers arose in the morning was at work

Which part of the passage gives you the best clue for getting the right answer? (A) Lines 1819: “At night before she went to sleep . . .” (B) Lines 1920: “. . . and during the day as she stood pinning dresses she wondered . . .” (C) Lines 1112: “But when she looked into the mirror in the mornings . . .” (D) Lines 2426: “What if they had survived and died of cold . . . while she was . . . dancing with British officers?” (E) I don’t know.

41.

When the author mentions his mother’s dancing with the British officers, he implies that his mother (A) compared her dancing to the suffering of her parents (B) had clearly put her troubles behind her (C) felt it was her duty to dance with them (D) felt guilty about dancing (E) regained the self-confidence she once had

*Celle is a small town in Germany.

37.

The author states that his mother thought about her parents when she

42.

Which words expressed in the passage lead us to the right answer? (A) (B) (C) (D) (E)

Line 24: “had survived” Lines 2425: “had died of cold or hunger” Line 21: “gotten past the Germans” Line 30: “like a robot” I don’t know.

That one citizen is as good as another is a favorite American axiom, supposed to express the very essence of our Constitution and way of life. But just what do we mean when we utter that platitude? One surgeon is not as good as 5 another. One plumber is not as good as another. We soon become aware of this when we require the attention of either. Yet in political and economic matters we appear to have reached a point where knowledge and specialized training count for very little. A newspaper reporter is sent 10 out on the street to collect the views of various passers-by on such a question as “Should the United States defend El Salvador?” The answer of the barfly who doesn’t even know where the country is located, or that it is a country, is

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quoted in the next edition just as solemnly as that of the college teacher of history. With the basic tenets of democracy— that all men are born free and equal and are entitled to life, liberty, and the pursuit of happiness—no decent American can possibly take issue. But that the opinion of one citizen on a technical subject is just as authoritative as that of 20 another is manifestly absurd. And to accept the opinions of all comers as having the same value is surely to encourage a cult of mediocrity.

47.

15

43.

44.

the myth of equality a distinction about equality the essence of the Constitution a technical subject knowledge and specialized training

48.

5

The author most probably included the example of the question on El Salvador (line 11) in order to 10

(A) move the reader to rage (B) show that he is opposed to opinion sampling (C) show that he has thoroughly researched his project (D) explain the kind of opinion sampling he objects to (E) provide a humorous but temporary diversion from his main point 46.

The distinction between a “barfly” and a college teacher (lines 1214) is that (A) (B) (C) (D) (E)

one is stupid, the other is not one is learned, the other is not one is anti-American, the other is not one is pro-El Salvadoran, the other is not I don’t know.

Which lines give the best clue to the answer to this question? (A) (B) (C) (D) (E)

Which is the best title for this passage? (A) “Equality—for Everyone, for Every Situation?” (B) “Dangers of Opinion and Knowledge” (C) “The American Syndrome” (D) “Freedom and Equality” (E) I don’t know.

45.

(A) some men are born to be masters; others are born to be servants (B) the Constitution has little relevance for today’s world (C) one should never express an opinion on a specialized subject unless he is an expert in that subject (D) every opinion should be treated equally (E) all opinions should not be given equal weight

Which phrase best expresses the main idea of this passage? (A) (B) (C) (D) (E)

The author would be most likely to agree that

15

20

25

30

Lines 35 Lines 46 Lines 1417 Lines 1822 I don’t know.

Mist continues to obscure the horizon, but above us the sky is suddenly awash with lavender light. At once the geese respond. Now, as well as their cries, a beating roar rolls across the water as if five thousand housewives have taken it into their heads to shake out blankets all at one time. Ten thousand housewives. It keeps up—the invisible rhythmic beating of all those goose wings—for what seems a long time. Even Lonnie is held motionless with suspense. Then the geese begin to rise. One, two, three hundred—then a thousand at a time—in long horizontal lines that unfurl like pennants across the sky. The horizon actually darkens as they pass. It goes on and on like that, flock after flock, for three or four minutes, each new contingent announcing its ascent with an accelerating roar of cries and wingbeats. Then gradually the intervals between flights become longer. I think the spectacle is over, until yet another flock lifts up, following the others in a gradual turn toward the northeastern quadrant of the refuge. Finally the sun emerges from the mist; the mist itself thins a little, uncovering the black line of willows on the other side of the wildlife preserve. I remember to close my mouth—which has been open for some time—and inadvertently shut two or three mosquitoes inside. Only a few straggling geese oar their way across the sun’s red surface. Lonnie wears an exasperated, proprietary expression, as if he had produced and directed the show himself and had just received a bad review. “It would have been better with more light,” he says; “I can’t always guarantee just when they’ll start moving.” I assure him I thought it was a fantastic sight. “Well,” he rumbles, “I guess it wasn’t too bad.”

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49.

In the descriptive phrase “shake out blankets all at one time” (line 5), the author is appealing chiefly to the reader’s (A) (B) (C) (D) (E)

53.

(A) (B) (C) (D) (E)

background sight emotions thoughts hearing 54.

50.

Which words preceding the above “descriptive phrase” in the passage give us a clue to the correct answer? (A) (B) (C) (D) (E)

51.

55.

tranquility excitement sadness bewilderment unconcern

Which word in the passage is most closely associated with the correct answer? (A) (B) (C) (D) (E)

mist spectacle geese refuge I don’t know.

Line 1 Lines 1617 Line 19 Line 30 I don’t know.

Judging from the passage, the reader can conclude that (A) (B) (C) (D) (E)

56.

are spectacular to watch are unpredictable disturb the environment produce a lot of noise fly in large flocks

Which line(s) gives us a clue to the correct answer? (A) (B) (C) (D) (E)

The mood created by the author is one of (A) (B) (C) (D) (E)

52.

“into their heads” “lavender light” “across the water” “a beating roar” I don’t know.

The main idea expressed by the author about the geese is that they

the speaker dislikes nature’s inconveniences the geese’s timing is predictable Lonnie has had the experience before both observers are hunters the author and Lonnie are the same person

Which gives us a clue to the right answer? (A) (B) (C) (D) (E)

Lines 910 Line 19 Lines 2122 Lines 2829 I don’t know.

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Section 2: Math Ability

In this section solve each problem, using any available space on the page for scratchwork. Then decide which is the best of the choices given and blacken the corresponding space on the answer sheet. The following information is for your reference in solving some of the problems. Circle of radius r : Area r 2; Circumference 2 r The number of degrees of arc in a circle is 360. The measure in degrees of a straight angle is 180. Definitions of symbols: is equal to is unequal to

is less than is greater than

is less than or equal to is greater than or equal to || is parallel to is perpendicular to

Triangle: The sum of the measures in degrees of the angles of a triangle is 180. If CDA is a right angle, then AB CD (1) area of ABC 2 (2) AC 2 AD 2 DC 2

NOTE: Figures that accompany problems in this test are intended to provide information useful in solving the problems. They are drawn as accurately as possible EXCEPT when it is stated in a specific problem that its figure is not drawn to scale. All figures lie in a plane unless otherwise indicated. All numbers used are real numbers.

1.

11 8 11 If P , then P 14 9 14 8 (A) 9 9 (B) 8 (C) 8 (D) 11 (E) 14

2.

How did you get your answer? 11 8 (A) I multiplied by , reducing first. 14 9 (B) I multiplied 11 8 and then divided the product by 14 9. 11 (C) I canceled from both sides of the equal 14 sign. (D) I guessed. (E) None of these.

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3.

Sarah is twice as old as John. Six years ago, Sarah was 4 times as old as John was then. How old is John now? (A) (B) (C) (D) (E)

4.


6.

9.

10.

11.

How did you get your answer? (A) I translated is to , what to a variable, of to , etc. Then I was able to set up an equation. (B) I just divided the two numbers and multiplied by 100 to get the percent. (C) I tried to remember how to work with is-of problems, putting the of over is or the is over of. (D) I guessed. (E) None of these.

4,730 5,000 9,860 9,950 10,000

How did you get your answer? (A) I multiplied 66 66, 2 34 66, and 34 34. (B) I approximated a solution. (C) I noticed that 662 2(34)(66) 342 had the form of a2 2ab b2 and set the form equal to(a b)2. (D) I guessed. (E) None of these.

1

/10 10 100 1,000 10,000

662 2(34)(66) 342 (A) (B) (C) (D) (E)

200 is what percent of 20? (A) (B) (C) (D) (E)

How did you get your answer? (A) I tried to calculate the area of the circle and the area of the triangle. (B) I used a special triangle or tried different triangles whose area was 15. (C) I subtracted 15 from 64. (D) I guessed. (E) None of these.

3 9 18 20 Cannot be determined.

(A) I substituted S for Sarah, for is, and J for John in the first sentence of the problem. Then I translated the second sentence into mathematical terms also. (B) I tried specific numbers for Sarah and/or John. (C) I racked my brain to figure out the ages but didn’t write any equations down. (D) I guessed. (E) None of these. 5.

8.

The average height of three students is 68 inches. If two of the students have heights of 70 inches and 72 inches respectively, then what is the height (in inches) of the third student? (A) (B) (C) (D) (E)

12.

60 62 64 65 66

How did you get your answer? (A) I used the following equation: (68 2) (68 4) x 68 68 68

7.

In this diagram, XYZ has been inscribed in a circle. If the circle encloses an area of 64, and the area of XYZ is 15, then what is the area of the shaded region? (A) (B) (C) (D) (E)


(B) (C) (D) (E)

Then I got: 68 68 (x 6) 68 68 68, and crossed off the two 68’s on both sides of the equation to come up with x 6 68. I was able to eliminate the incorrect choices without figuring out a complete solution. (70 72 x) I got the equation 68, then 3 solved for x. I guessed. None of these.

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13.

If 0 x 1, then which of the following must be true? (A) (B) (C) (D) (E)

14.

I only II only I and II only II and III only I, II, and III

II. x 1 0 III. x2 x


16.

an odd integer an even integer the cube of an integer the square of an integer the product of an integer and 3

If p is a positive integer, which could be an odd integer? (A) (B) (C) (D) (E)

2p 2 p3 p p2 p p2 p 7p 3

In this figure, two points, B and C, are placed to the right of point A such that 4AB 3AC. The value of BC/AB 1 (A) equals 3 2 (B) equals 3 3 (C) equals 2 (D) equals 3 (E) Cannot be determined.

20.

How did you get your answer? (A) I drew points B and C on the line and labeled AB as a and BC as b and then worked with a and b. (B) I substituted numbers for AB and AC. (C) I drew points B and C on the line and worked with equations involving BC and AB. (D) I guessed. (E) None of these.

How did you get your answer? (A) I translated the statement into the form x3 (x 1)3 ________ and tried to see what I would get. (B) I tried numbers like 1 and 2 for the consecutive integers. Then I calculated the sum of the cubes of those numbers. I was able to eliminate some choices and then tried some other numbers for the consecutive integers to eliminate more choices. (C) I said, of two consecutive positive integers, one is even and therefore its cube is even. The other integer is odd, therefore its cube is odd. An odd an even is an odd. (D) I guessed. (E) None of these.

17.

19.

The sum of the cubes of any two consecutive positive integers is always (A) (B) (C) (D) (E)

How did you get your answer? (A) I plugged in a number or numbers for p and started testing all the choices, starting with Choice A. (B) I plugged in a number or numbers for p in each of the choices, starting with Choice E. (C) I looked at Choice E first to see if 7p 3 had the form of an even or odd integer. (D) I guessed. (E) None of these.

I. 2x 2

(A) I plugged in only one number for x in I, II, and III. (B) I plugged in more than one number for x and tried I, II, and III using each set of numbers. (C) I used the fact that 0 x and x 1 and manipulated those inequalities in I, II, and III. (D) I guessed. (E) None of these. 15.

18.

21.

A man rode a bicycle a straight distance at a speed of 10 miles per hour. He came back the same way, traveling the same distance at a speed of 20 miles per hour. What was the man’s total number of miles for the trip back and forth if his total traveling time was one hour? (A) 15 1 (B) 13 3 1 (C) 7 2 2 (D) 6 3 1 (E) 6 3

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22.

How did you answer this question?

26.

(A) I solved for the value of y from y8 4. Then I 3 substituted that value of y in y7 . x (B) I took the seventh root of y in the second equation. (C) I divided the first equation by the second equation to get y alone in terms of x. (D) I guessed. (E) None of these.

(A) I used Rate Time Distance and plugged in my own numbers. (B) I averaged 10 and 20 and worked from there. (C) I called the times going back and forth by two different unknown variables but noted that the sum of these times was 1 hour. (D) I guessed. (E) None of these. 23.

If the symbol is defined by the equation 27.

ab a b ab 1 for all a and b, then (3) 3 5 (A) 3 11 (B) 3 13 (C) 5 (D) 4 (E) 5

24.

28.

25.

3 If y8 4 and y7 , what is the value of y in terms x of x? 4x (A) 3 3x (B) 4 4 (C) x x (D) 4 12 (E) x

5x 8y If 4x 5y 10 and x 3y 8, then 3 (A) 18 (B) 15 (C) 12 (D) 9 (E) 6 How did you get your answer? (A) I solved both simultaneous equations for x and for y, then substituted the values of x and y into (5x 8y) . 3 (B) I tried numbers for x and for y that would satisfy the first two equations. (C) I added both equations to get 5x 8y. Then I divided my result by 3. (D) I guessed. (E) None of these.

How did you get your answer? 1 (A) I played around with the numbers and 3 3 to get my answer. I didn’t use any substitution method. 1 (B) I substituted in ab a b ab, for a 3 and 3 for b. (C) I worked backward. (D) I guessed. (E) None of these.


29.

The circle with center A and radius AB is inscribed in the square here. AB is extended to C. What is the ratio of AB to AC? (A) 2 2 (B) 4 2 1 (C) 2 2 (D) 2 (E) None of these.

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30.

How did you get your answer? (A) I approximated the solution. I looked to see what the ratio of AB to AC might be from the diagram. Then I looked through the choices to see which choice was reasonable or to eliminate incorrect choices. (B) I saw a relationship between AB and AC but didn’t draw any other lines. (C) I dropped a perpendicular from A to one of the sides of the square, then worked with the isosceles right triangle. I also labeled lengths AB by a single letter, and BC by another single letter. (D) I guessed. (E) None of these.

31.

34.

(A) I tried to first find angles A and D. (B) I drew a perpendicular from A to DC and labeled BC as an unknown (x or y, etc.). (C) I labeled BC as an unknown (x or y, etc.) but did not draw a perpendicular line from A to DC, (D) I guessed. (E) None of these. 35.

Which of the angles below has a degree measure that can be determined? (A) (B) (C) (D) (E)

In the accompanying figure, side BC of triangle ABC is extended to D. What is the value of a? (A) (B) (C) (D) (E)


WOS SOU WOT ROV WOV

15 17 20 24 30

(Note: Figure is not drawn to scale.) (Note: Figure is not drawn to scale.) 32.

How did you get your answer? (A) (B) (C) (D) (E)

33.

I first said that 2y 6y a 180. I first said that 6y 3y 180, then solved for y. I first said 3y 2y a. I guessed. None of these.

What is the perimeter of the accompanying figure if B and C are right angles? (A) (B) (C) (D) (E)

14 16 18 20 Cannot be determined. (Note: Figure is not drawn to scale.)

36.

How did you get your answer? (A) I first said that 4a 2b 360, got 2a b 180, then looked through the choices. (B) I looked through the choices first. (C) I knew that the sum of the angles added up to 360 degrees but didn’t know where to go from there. (D) I guessed. (E) None of these.

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This is the end of the Strategy Diagnostic Test for the SAT. You’ve answered the questions in both the Verbal and Math sections, and you’ve recorded how you arrived at each answer. Now you’re ready to find out how you did. Go right to the table that follows for answer checking, diagnosis, and prescription. Remember, the questions are in pairs—the oddnumbered ones are the questions themselves, the evennumbered ones, the approach you used to solve the questions. If either or both of your answers—solution and/or approach—fail to correspond to the answers

given in the table, you should study the strategy for that pair. The table also gives the SAT score increase that’s possible if you master that strategy. The approximate time it should take to answer a particular question is also supplied. By using the best strategies throughout the actual SAT, you should increase accuracy, make the best use of your time, and thus improve your score dramatically. Note: If the even-numbered answer (for questions 2, 4, 6, etc.) does not match with your answer, you may want to look at the approach described in the answer as you may be able to use that approach with other questions.

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STRATEGY DIAGNOSTIC TEST ANSWER AND DIAGNOSTIC TABLE Section 1 Verbal Ability *If either or both of your answers do not match the answers to the left, then refer to this strategy:

Possible score increase if strategy is learned

Estimated time to solve each oddnumbered question (in seconds)

Question number

Answer

1 2

D A

Sentence Completion 1, p. 118

70

20

3 4

B C


40

40

5 6

E B


40

30

7 8

C B


100

30

9 10

E C


100

40

11 12

C B


100

30

13 14

A B

Vocabulary 1, p. 148

60

20

15 16

E B


60

20

17 18

B B


60

20

19 20

C B


30

20

21 22

D B


60

20

23 24

E B


30

20

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STRATEGY DIAGNOSTIC TEST ANSWER AND DIAGNOSTIC TABLE (Continued) Section 1 Verbal Ability *If either or both of your answers do not match the answers to the left, then refer to this strategy:



Question number

Answer

25 26

B B


30

20

27 28

B B,C


30

20

29 30

A B


30

20

31 32

D B,C,D


30

20

33 34

E B


60

30

35 36

B B


30

20

37 38

B B

Reading Comprehension 1, 2, pp. 133, 136

200

15

39 40

E B


200

20

41 42

D B


200

20

43 44

B B


200

20

45 46

D B


200

30

47 48

E D


200

30

49 50

E D


200

20

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STRATEGY DIAGNOSTIC TEST ANSWER AND DIAGNOSTIC TABLE (Continued) Section 1 Verbal Ability *If either or both of your answers do not match the answers to the left, then refer to this strategy:



Question number

Answer

51 52

B B


200

20

53 54

A B


200

20

55 56

C D


200

30

Section 2 Math Ability 1 2

A C

Math 1, p. 69

20

10

3 4

B A

Math 2, p. 71

60

40

5 6

D A

Math 2, p. 71

60

30

7 8

C C

Math 3, p. 77

10

20

9 10

E C

Math 4, p. 80

20

40

11 12

B C

Math 5, p. 82

20

40

13 14

E C

Math 6, p. 85

140

50

15 16

A B

Math 7, p. 88

30

40

17 18

E B or C

Math 8, p. 90

20

30

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STRATEGY DIAGNOSTIC TEST ANSWER AND DIAGNOSTIC TABLE (Continued) Section 2 Math Ability *If either or both of your answers do not match the answers to the left, then refer to this strategy:



Question number

Answer

19 20

A A

Math 14, p. 102

50

40

21 22

B C

Math 9, p. 92

10

60

23 24

A B

Math 11, p. 96

30

50

25 26

A C

Math 12 or 13, pp. 98, 100

50

30

27 28

E C

Math 13, p. 100

20

20

29 30

D C

Math 14, 18, pp. 102, 112

80

50

31 32

C B

Math 17, 18, pp. 109, 112

160

40

33 34

C B

Math 14, 18, pp. 102, 112

80

30

35 36

C A

Math 17, p. 109

140

40

*Note: The solution to the odd-numbered question appears in the strategy section listed.

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PA R T 2

THE SHORTEST SAT TEST— 16 QUESTIONS TO APPROXIMATE YOUR SAT SCORE And the Exact Strategies You Need to Improve Your Score Although it shouldn’t take you more than 40 seconds to answer each verbal (Critical Reading) and writing question and 1 minute to answer each math question, you may take this test untimed and still get a fairly accurate prediction. Note: The PSAT score is approximately calculated by dividing the SAT score by 10 and is used for National Merit Scholarships. The top schools require SAT scores in the 1800 range. Following is a test that can determine if you have the goods—and it won’t take you more than 15 minutes.

*As syndicated in The Washington Post and in other national newspapers.

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24 • THE SHORTEST SAT TEST—16 QUESTIONS TO APPROXIMATE YOUR SAT SCORE

Verbal (Critical Reading)

Allow 7 minutes for this part.

Sentence Completions

Reading Comprehension

Fill in the blank(s) with the appropriate choice:

Read the following passage. Then answer the questions:

1.

(A) (B) (C) (D) (E) 2.

1

accepted . . . refused concluded . . . consented denounced . . . declined asserted . . . acceded rejected . . . preferred

4.

interest . . . enthralled power . . . taken intensity . . . shocked greatness . . . gratified strength . . . bored

5.

6.


phenomena of the Pacific coastline poisons that affect man toxic plants in the sea characteristics of plankton phenomena of the sea

It can be assumed that “plankton” in line 5 are (A) (B) (C) (D) (E)

24

strangeness color calamity potency powerful odor

The paragraph preceding the one in the passage most probably discussed the (A) (B) (C) (D) (E)

7.

swim in poisonous water feed on poisonous plants or animals change their feeding habits give off a strange glow take strychnine into their systems

In the context of the passage, the word virulence in line 4 means (A) (B) (C) (D) (E)

Richard Wagner was frequently intolerant; moreover, his strange behavior caused most of his acquaintances to _______ the composer whenever possible. (A) (B) (C) (D) (E)

Fish and shellfish become toxic when they (A) (B) (C) (D) (E)

In spite of the ______ of his presentation, many people were _______ with the speaker’s concepts and ideas. (A) (B) (C) (D) (E)

3.

Sometimes the meaning of glowing water is ominous. Off the Pacific Coast of North America, it may mean that the sea is filled with a minute plant that contains a poison of strange and terrible virulence. About four days after this minute 5 plant comes to alter the coastal plankton, some of the fishes and shellfish in the vicinity become toxic. This is because in their normal feeding, they have strained the poisonous plankton out of the water.

The instructor displayed extreme stubbornness; although he ______ the logic of the student’s argument, he _______ to acknowledge her conclusion as correct.

fish and shellfish small plants or animals sand deposits land parasites glacier or rock formations

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THE SHORTEST SAT TEST—16 QUESTIONS TO APPROXIMATE YOUR SAT SCORE • 25

Math

Allow 7 minutes for this part. Answer the following questions: 1.

If 2x 3y 4 and y 2, find the value of x. (A) 2 (B) 1 (C) 0 (D) 1 (E) 2

2.

If x y 7 and xy 4, then find the value of x2 y2.

a/(a 1) 1/(a 1) a6 a5 a5 a6

6.

If y 2q 15, q 2p 5 and p 2y 7, then find the value of p q y.

7.

On a street with 25 houses, 10 houses have fewer than 6 rooms, 10 houses have more than 7 rooms, and 4 houses have more than 8 rooms. What is the total number of houses on the street that are either 6-, 7-, or 8-room houses?

Sarah is twice as old as John. Six years ago Sarah was four times as old as John was then. In years, how old is John now? (A) (B) (C) (D) (E)

3 9 18 20 Cannot be determined

(Note: Figure is not drawn to scale.) 4.

5.

Where a 1, (a7 a6)/(a 1) (A) (B) (C) (D) (E)

3.

In the following questions you must find an answer without referring to choices:

The area of the above figure ABCD (A) (B) (C) (D) (E)

is 36 is 108 is 156 is 1872 Cannot be determined

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Writing

Allow 1 minute for this part. Indentifying Sentence Errors:

Improving Sentences:

Which part (A, B, C, or D) in the sentence below is incorrect? Choose E if there is no error.

Which choice correctly replaces the sentence below? He never has and never will keep his word.

If any signer of the Constitution (A) was to return to life (B) for a day, his opinion (C) of our amendments (D) would be interesting.

(A) (B) (C) (D) (E)

He never has and never will keep his word. He has never yet and never will keep his word. He has not ever and will not keep his word. He never has or will keep his word. He never has kept and he never will keep his word.

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THE SHORTEST SAT TEST—16 QUESTIONS TO APPROXIMATE YOUR SAT SCORE • 27

Answers

Verbal (Critical Reading)

Math

1. A

1. D

2. E

2. E

3. C

3. B

4. B

4. A

5. D

5. 41

6. E

6. 9

7. B

7. 11

Writing 1. A 2. E

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Shortest SAT Test What You Did Wrong, Explanatory Answers and Scoring, Strategies and Basic Skills Needed to Improve Now go to the website www.sourcebookscollege.com/gruberquiz and record your answers in the grid given on the site. Even though you may have gotten a wrong answer, you may have come close to the answer or done part of it correctly. The computer will assess your patterns and give you: 1. Your approximate SAT score. 2. Why you got the questions wrong, what you should use to get a question right, and a detailed explanation of exactly the best way you should answer the question.

3. Each answer that will lead you to the exact page of this book that will teach you the strategy and basic skill you need to use for this type of question. 4. The page number of this book where you can find similar sample questions to test your ability using the strategy and basic skill.

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PA R T 3

THE 101 MOST IMPORTANT MATH QUESTIONS YOU NEED TO KNOW HOW TO SOLVE Take This Test to Determine Your Basic (as Contrasted with Strategy) Math Weaknesses (Diagnosis and Corrective Measures Follow Test)

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30 • THE 101 MOST IMPORTANT MATH QUESTIONS YOU NEED TO KNOW HOW TO SOLVE

101 Math Questions Answer Sheet

A. Fractions 1. 2. 3. 4. 5.

B. Even–Odd Relationships 6. 7. 8. 9. 10. 11. 12.

C. Factors 13. 14. 15. 16. 17. 18. 19. 20. 21.

D. Exponents 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32.

E. Percentages 33. 34. 35.

F. Equations 36. 37. 38. 39. 40.

G. Angles 41. 42. 43. 44.

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THE 101 MOST IMPORTANT MATH QUESTIONS YOU NEED TO KNOW HOW TO SOLVE • 31

H. Parallel Lines 45. 46. 47. 48. 49. 50. 51.

I. Triangles 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65.

J. Circles 66. 67. 68. 69. 70.

K. Other Figures 71. 72. 73. 74. 75. 76. 77. 78. 79. 80.

L. Number Lines 81. 82.

M. Coordinates 83. 84. 85.

N. Inequalities 86. 87. 88. 89. 90. 91.

O. Averages 92. 93.

P. Shortcuts 94. 95. 96. 97. 98. 99. 100. 101.

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101 Math Questions Test Following are the 101 most important math questions you should know how to solve. After you take the test, check to see whether your answers are the same as those described, and whether or not you answered the question in the way described. After a solution, there is usually (where appropriate) a rule or generalization of the math concept just used in the solution to the particular problem. Make sure that you understand this generalization or rule, as it will apply to many other questions. Remember that these are the most important basic math questions you need to know how to solve. Make sure that you understand all of them before taking any standardized math test such as the SAT. DO NOT GUESS AT ANY ANSWER! LEAVE ANSWER BLANK IF YOU DON’T KNOW HOW TO SOLVE.

A. Fractions 1.

a b c

4.

ab (A) c ac (B) b a (C) bc (D) abc (E) None of these. 2.

1 1 y (A) y (B) y2 1 (C) y (D) infinity (E) None of these.

3.

a b c a (A) bc ac (B) b ab (C) c (D) abc (E) None of these.

1 x y (A) xy x (B) y y (C) x x (D) y

2

(E) None of these.

5.

a b b a b2 (A) 2 a a2 (B) b2 (C) 1 a (D) b (E) None of these.

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B. Even–Odd Relations (Note: CBD Cannot Be Determined) 6.

(A) (B) (C) (D) (E)

ODD INTEGER ODD INTEGER (A) odd integer (B) even integer (C) no integer or CBD

7.

14. (x 3)(x 2)

15.

(A) odd integer (B) even integer (C) no integer or CBD 16. 8.

EVEN INTEGER EVEN INTEGER

ab b2 bc a b2 c a2 b2 ca ab b2 ac bc None of these.

EVEN INTEGER or EVEN INTEGER 17.

(A) odd integer (B) even integer (C) no integer or CBD 10.

xy 5y 6 xy 2x 3y 6 xy6 xy 3y 2x 6 None of these.

(a b)(b c) (A) (B) (C) (D) (E)

(A) odd integer (B) even integer (C) no integer or CBD 9.

(x 3)(y 2) (A) (B) (C) (D) (E)

ODD INTEGER or ODD INTEGER

x2 x 6 x2 x 5 x2 x 6 2x 1 None of these.

(A) (B) (C) (D) (E)

(ODD INTEGER)ODD POWER (A) odd integer (B) even integer (C) CBD

18. EVEN POWER

11. (EVEN INTEGER)

(A) odd integer (B) even integer (C) CBD 19.

C. Factors 13. (x 3)(x 2)

(A) (B) (C) (D) (E)

x2 5x 6 x2 6x 5 x2 x 6 2x 5 None of these.

20.

a2 2ab b2 a2 b2 a2 b2 ab 2a 2b None of these.

(a b) (A) (B) (C) (D) (E)

(A) odd integer (B) even integer (C) CBD

a2 2ba b2 a2 2ba b2 a2 b2 0 None of these.

(a b)2 (A) (B) (C) (D) (E)

12. (EVEN INTEGER)ODD POWER

(a b)(a b)

ab ab ab ba None of these.

a(b c) (A) (B) (C) (D) (E)

ab ac ab c abc ab bc None of these.

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34 • THE 101 MOST IMPORTANT MATH QUESTIONS YOU NEED TO KNOW HOW TO SOLVE 21. a(b c)

(A) (B) (C) (D) (E)

ab ac ab ac ac ab ab ac None of these.

D. Exponents 22.

(A) (B) (C) (D) (E) 24.

(A) (B) (C) (D) (E) 26.

29.

7

30.

31.

ab a7b a7b7 a14b14 None of these. 8

c a

a8 (A) c8 a8 (B) c a (C) 8 c a7 (D) c

(E) None of these.

a3 b5

(a3)5 (A) (B) (C) (D) (E)

a10 a7 a3 (2a)10 None of these.

(ab)7

(ab)4 (ab)8 (ab)16 (ab)12 None of these.

b5 (A) 3 a (B) (ab)2 (C) (ab) 15 a3 (D) b5 (E) None of these.

104 105 106 107 None of these.

a2 a5 (A) (B) (C) (D) (E)

25.

28.

1000 10,000 100,000 1,000,000 None of these.

107076.5 1.070765

a4 b4 (A) (B) (C) (D) (E)

105 (A) (B) (C) (D) (E)

23.

27.

32.

a8 a2 a15 a243 None of these.

2a3 2 (A) 3 a (B) 2a3 3 (C) 2 a (D) a6 (E) None of these. 1 2am an 3 2 mn (A) a 3 2 am (B) 3 an 2 (C) amn 3 2 (D) amn 3 (E) None of these. 32 32 41 60 1 (A) 8 9 1 (B) 12 9 1 (C) 13 9 1 (D) 14 9 (E) None of these.

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E. Percentages 33.

39.

15% of 200 (A) (B) (C) (D) (E)

(A) (B) (C) (D) (E)

3 30 300 3,000 None of these. 40.

34.

What is 3% of 5? 5 (A) % 3 (B) 15 3 (C) 20 3 (D) 5 (E) None of these.

35.

What percent of 3 is 6? (A) (B) (C) (D) (E)

50 20 200 1 /2 None of these.

What is the value of x and y if x 2y 2 and 2x y 4? x 2, y 0 x 0, y 2 x 1, y 2 x 0, y 2 None of these.

x 7 If , x 5 12 35 (A) 12 12 (B) 35 7 (C) 60 60 (D) 7 (E) None of these.

G. Angles (Vertical, Supplementary) Questions 4142 refer to the diagram below:

F. Equations 36.

If y2 16, y (A) (B) (C) (D) (E)

37.

If x y 10, y (A) (B) (C) (D) (E)

38.

4 only 4 only or 4 or 8 None of these.

x 10 10 x 10 x 10 None of these.

What is the value of x if x 4y 7 and x 4y 8? (A) 15 15 (B) 2 (C) 7 7 (D) 2 (E) None of these.

41. a

(A) (B) (C) (D) (E) 42.

30 150 45 90 None of these.

b (A) (B) (C) (D) (E)


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Question 43 refers to the diagram below:

46.

b (A) (B) (C) (D) (E)

43.

ab (A) (B) (C) (D) (E)

47.

c (A) (B) (C) (D) (E)

155 165 180 145 None of these. 48.

44.

(A) (B) (C) (D) (E)

180 240 360 540 None of these.

50.

Questions 4551 refer to the diagram below:

51.

a (A) (B) (C) (D) (E)

50 130 100 40 None of these.

50 130 100 40 None of these.

g (A) (B) (C) (D) (E)

45.

50 130 100 40 None of these.

f (A) (B) (C) (D) (E)

H. Angles (Parallel Lines)

50 130 100 40 None of these.

e (A) (B) (C) (D) (E)

What is the value of a b c d e f g h in the diagram above?

50 130 100 40 None of these.

d (A) (B) (C) (D) (E)

49.

50 130 100 40 None of these.

50 130 100 40 None of these.

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I. Triangles

55.

52.

(Note: Figure is not drawn to scale.) (Note: Figure is not drawn to scale.)

a (A) 70 (B) 40 xy (C) 70 (D) Cannot be determined. (E) None of these.

In the triangle above, x (A) (B) (C) (D) (E)

53.


56.

(Note: Figure is not drawn to scale.) x

In the triangle above, if B A, then

(A) 3 50 (B) 3 (C) 32 (D) Cannot be determined. (E) None of these.

ba ba b a A relation between b and a cannot be determined. (E) None of these.

(A) (B) (C) (D)

54. 57.

(Note: Figure is not drawn to scale.) Which is a possible value for a? (A) (B) (C) (D) (E)


In the triangle above, if b a, then BA BA B A A relation between B and A cannot be determined. (E) None of these.

(A) (B) (C) (D)

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58.

61.

(Note: Figure is not drawn to scale.)


In the right triangle above as shown, x


(A) (B) (C) (D) (E)

59.



(Note: Figure is not drawn to scale.) (Note: Figure is not drawn to scale.)


42 8 4 a number between 1 and 4 None of these.

62.

The perimeter of the triangle ABC is (A) (B) (C) (D) (E)

60. 63.

The area of triangle ABC is (A) (B) (C) (D) (E)

In the diagram above, x (A) (B) (C) (D) (E)



170 85 168 84 None of these.

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64.

The area of the triangle is (A) (B) (C) (D) (E)

65.

68.

In the diagram above, x

6 7 12 any number between 5 and 7 None of these.

(A) (B) (C) (D) (E)

The perimeter of the triangle is (A) (B) (C) (D) (E)

7 12 15 any number between 7 and 12 None of these.

70 35 90 a number that cannot be determined None of these.

69.

J. Circles Questions 6667 refer to the diagram below: In the diagram above, x (A) (B) (C) (D) (E) 66.

The area of the circle is (A) (B) (C) (D) (E)

67.


70.

49 49p 14p 196p None of these.

The circumference of the circle is (A) (B) (C) (D) (E)

14p 7p 49p 14 None of these.

In the diagram above, y (A) (B) (C) (D) (E)


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K. Other Figures

75.

What is DB if AC 10? (A) (B) (C) (D) (E)


4 6 8 10 12


71.

The area of the figure is (A) (B) (C) (D) (E)

72.


76.

(A) (B) (C) (D) (E)

The perimeter of the figure is (A) (B) (C) (D) (E)


The area of the figure is

77.

The perimeter of the figure is (A) (B) (C) (D) (E)

Questions 7375 refer to the figure below:



Questions 7879 refer to the figure below:

ABCD is a rectangle 73.

What is BC if AD 6? (A) (B) (C) (D) (E)

74.

4 6 8 10 12

What is DC if AB 8? (A) (B) (C) (D) (E)

4 6 8 10 12

ABCD is a square; AC 3 78.

What is the area of the square? (A) (B) (C) (D) (E)


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79.

What is the perimeter of the square? (A) (B) (C) (D) (E)

80.


M. Coordinates Questions 8385 refer to the diagram below:

The volume of the rectangular solid below is (A) (B) (C) (D) (E)


83.

(A) (B) (C) (D) (E)

L. Number Lines Questions 8182 refer to the diagram below:

81.

82.

1 b 2 2b0 1b0 3 b 3 b0

negative? (A) (B) (C) (D) (E) 85.

a 2 1 a 2 0 a 2 1 a 0 a 3

1 2 3 4 5

If a 3, b 4, what is x? (A) (B) (C) (D) (E)

Which defines the range in values of a best? (A) (B) (C) (D) (E)

1 2 3 4 5

84. How many of the variables a, b, c, d, e, f, g, h are

Which defines the range in values of b best? (A) (B) (C) (D) (E)

How many of the variables a, b, c, d, e, f, g, h are positive?


N. Inequalities Note: Any variable can be positive or negative or 0. 86.

If x y, then 4x 4y (A) always (B) sometimes (C) never

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87.

If x y z, then y z x (A) always (B) sometimes (C) never

88.

P. Shortcuts 94.

If 4 x, then 4 x (A) always (B) sometimes (C) never

89.

If m n, where q is any number, then qm qn (A) always (B) sometimes (C) never

90.

95.

If x y and p q, then x p y q (A) always (B) sometimes (C) never

91.

If x y and p q, then xp qy (A) always (B) sometimes (C) never

96.

What is the average of 30, 40, and 80? (A) (B) (C) (D) (E)

93.


What is the average speed in mph of a car traveling 40 miles for 4 hours? (A) (B) (C) (D) (E)

160 10 120 30 None of these.

3 7 Add: : 5 12 11 (A) 1 60 13 (B) 1 60 15 (C) 1 60 10 (D) 17 (E) None of these. 7 3 Subtract: : 12 5 1 (A) 60 3 (B) 60 11 (C) 1 60

O. Averages 92.

Which is greater? Don’t calculate a common denominator! 3 7 or 7 16 7 (A) 16 3 (B) 7 (C) They are equal. (D) A relationship cannot be determined.

4 (D) 7 (E) None of these. 97.

4 250 (A) (B) (C) (D) (E)

.016 .04 .004 .025 None of these.

Note: Do not divide 250 into 4 in the above question!

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98.

What is c if

100.

Find the value of

abc ab 200 and 80 ? 2 3 (A) (B) (C) (D) (E) 99.

160 140 120 100 None of these.

What is the value of 95 75 95 74? (Don’t multiply 95 75 or 95 74! ) (A) (B) (C) (D) (E)

140 15 (Don’t multiply 140 15! ) 57


(A) (B) (C) (D) (E) 101.


What is the value of 70 21 36 4? (A) 211,680 (B) 211,681 (C) 211,682 (D) 211,683 (E) 211,684 (Don’t multiply! )

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101 Math Questions: Answers, Diagnosis, Solutions, Generalizations, Rules

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101 Math Questions: Answers

A. Fractions 1. 2. 3. 4. 5.

B A A C B

B. Even–Odd Relationships 6. 7. 8. 9. 10. 11. 12.

A B B B A B B

C. Factors 13. 14. 15. 16. 17. 18. 19. 20. 21.

A C B D C A D A C

D. Exponents 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32.

C B B C A A A C A B D

E. Percentages 33. B 34. C 35. C

F. Equations 36. 37. 38. 39. 40.

C A B A A

G. Angles 41. 42. 43. 44.

B A A C

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H. Parallel Lines 45. 46. 47. 48. 49. 50. 51.

B A B B A A B

I. Triangles 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65.

A A B B B C B C C B B D A B

J. Circles 66. 67. 68. 69. 70.

B A B A C

K. Other Figures 71. 72. 73. 74. 75. 76. 77. 78. 79. 80.

C B B C D B B A B B

L. Number Lines 81. C 82. B

M. Coordinates 83. D 84. D 85. C

N. Inequalities 86. 87. 88. 89. 90. 91.

A A A B A B

O. Averages 92. C 93. B

P. Shortcuts 94. 95. 96. 97. 98. 99. 100. 101.

A A A A A D C A

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BASIC SKILLS MATH DIAGNOSIS

Math area

Total questions

A. Fractions B. Integers C. Factors D. Exponents E. Percentages F. Equations G. Angles H. Angles (parallel lines) I. Triangles J. Circles K. Other Figures L. Number Lines M. Coordinates N. Inequalities O. Averages P. Shortcuts *Answer sheet is on pages 4546.

5 7 9 11 3 5 4 7 14 5 10 2 3 6 2 8

*If you got any of the answers to the following questions wrong, study answers to those questions.

Page in text for review

Complete Math Refresher: Refer to the sections of the Math Refresher (Part 6, starting on page 165) shown here for a refresher on the applicable rules.

15 612 1321 2232 3335 3640 4144 4551 5265 6670 7180 8182 8385 8691 9293 94101

48 48 49 4950 50 5051 51 51 5154 55 5556 56 56 57 57 5758

101112, 123128 603611 409 429430 106, 107, 114 406409 500503 504 505516, 306308 524529, 310311 517523, 303305, 309, 312316 410a 410b418 419428 601 128, 609

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Solutions, Generalizations, Rules

A. Fractions

Alternate way: a a a2 a2 a b b b b b a b b b a a a a

1. (B)

ac c a a b b b T c ERT Y O

a2 b b a2 b b 2 b

L INV TIP MUL

Alternate way: ac ac c a a b b c b b c c c c 2. (A)

O

y 1 1 y 1 1 T y ERT LY

B. Even–Odd Relationships 6.

3 3 9; 5 5 25 7.

INV TIP MUL

3.

(A)

a b c =

a a b b b b a cb cb cb

8.

T LY O

10.

O

(A) (ODD)ODD ODD 33 3 3 3 27 (odd) 127 1 odd

5. (B)

INVER IPLY T MUL

(B) EVEN or EVEN EVEN 6 2 8; 10 4 6

L MU

a b a a a2 2 b b b b a T T

(B) EVEN EVEN EVEN 2 2 4; 4 2 8

(C) y y 1 1 x x x y INVE RTTIP

(B) ODD or ODD EVEN 538 532

9. 4.

(A) ODD ODD ODD

11.

(B) (EVEN)EVEN EVEN 22 4(even); 42 16 (even)

12.

(B) (EVEN)ODD EVEN 23 2 2 2 8 (even) 41 4 (even)

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C. Factors 13.

20.

a(b c) ab ac

(A) (x 3)(x 2) x2 . . . (x 3)(x 2) x2 3x 2x . . .

21.

(C) a(b c)

(x 3)(x 2) x 3x 2x 6

a(b c) ab a(c)

(x 3)(x 2) x2 5x 6

ab ac

2

14.

(A) a(b c)

(C) (x 3)(x 2) x2 . . .

ca ab

D. Exponents (Solutions)

(x 3)(x 2) x 2x 3x . . . 2

22. (C) 105 100000

(x 3)(x 2) x2 2x 3x 6

5 zeroes

(x 3)(x 2) x2 x 6 15.

23.

(B) (x 3)( y 2) xy . . .

(B) 107076.5 1 0 7 0 7 0 . 5 5 4 3 2 1 5 1.070765 10

(x 3)( y 2) xy 2x 3y . . . (x 3)( y 2) xy 2x 3y 6 16.

24.

(B) ADD EXPONENTS

25.

(C) (ab)7 a7b7

(D) (a b)(b c) ab . . . (a b)(b c) ab ac b2 . . .

(ab)m ambm

(a b)(b c) ab ac b2 bc 26. 17.

(C) (a b)(a b)

(a b)(a b) a2 ab ba . . .

a8 a ; c c8

m

(A) a4 b4 (ab)4 ; am bm (ab)m

28.

(A)

(a b)(a b) a2 ab ba b2

b5 a3 b5 3 a

MEMORIZE

bn am bn m a

(A)(a b)2 (a b)(a b) (a b)(a b) a2 . . .

29.

(a b)(a b) a2 ab ba . . . (a b)(a b) a2 ab ba b2 (a b)2 a2 2ab b2 19.

(D) (a b) a ( b) (a b) a b (a b) b a

am m c

27.

(a b)(a b) a2 ab ba b2

18.

8

a c

(a b)(a b) a2 . . .

(a b)(a b) a2 b2

(A)

30.

MEMORIZE

(A)

2 2a 3 3 a a axb b x

MEMORIZE

1 Since an an

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31.

F. Equations

(B) 2am 1 an 2 aman 3 3

36.

16

y2 16

2 am 2 am n or 3 an 3 32.

(C) y 2 y 4

Note: y means the positive square root of y. That is, the positive number that when multiplied by itself will give you the value of y.

(D) 3 3 3 9 1 1 3 2 2 9 3 2

(y) (y) y

4 4 1

60 1 (any number to 0 power 1)

37.

32 32 41 60 9 1 4 1 14 1 9 9

E. Percentages

x 10 y

Questions 33–35 Translate is ➝ of ➝ (times) percent(%) ➝

38.

100 what ➝ x (or y, etc.)

33.

(B) 15%

of 200

↓↓

↓ ↓ ↓

2x 15 5 x 1 2 39.

15 20 0 30 0 1 0 (C) What is 3% of 5 ?

2x 4y 4

3 15 x 20 100 (C) What percent of 3 is 6 ?

↓

x

100

x 3 6 100 3x 6 100 3x 600 x 200

↓ ↓ ↓ ↓

1 2

Subtract 2 from 3 :

x 3 5 100 3 5 x 100

↓

(A) x 2y 2 2x y 4 Multiply 1 by 2: 2(x 2y) 2(2) We get: 2x 4y 4

↓ ↓ ↓ ↓ ↓ ↓

35.

(B) Add equations: x 4y 7 x 4y 8 2x 4y 4y 15

15 200 100 15 200 100

34.

(A) x y 10 Add y: x y y 10 y x 10 y Subtract 10: x 10 10 10 y

3

6

(2x y 4)

3 2

0 5y 0 y0

4

Substitute: 4 into either 1 or 2 : In 1 : x 2y 2 x 2(0) 2 x2

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40.

(A) x 7 5 12 Cross-multiply x: x 5

H. Parallel Lines (Angles) Questions 45–51 7 12

12x 35 Divide by 12: 12x 35 12 12

45.

a 130

1 x 35 2 1 12 12

G. Angles (Vertical and Supplementary) This diagram refers to questions 41–42.

(B) a 50 180

46.

(A) b 50 (vertical angles)

47.

(B) c a (vertical angles) 130

48.

(B) d c (alternate interior angles are equal) 130

49.

(A) e b (alternate interior angles) 50

50. 41.

42.

43.

(B) a° and 30° are supplementary angles (they add up to 180°). So a 30 180; a 150 . (A) b° and 30° are vertical angles (vertical angles are equal). So b 30 . (A) This diagram refers to questions 43–44.

(A) f e (vertical angles) 50

51.

(B) g d (vertical angles) 130

I. Triangles 52.

(A)

(Note: Figure is not drawn to scale.) a°, b° and 25° make up a straight angle which is 180°. a b 25 180 a b 180 25 a b 155 44.

(C) The sum of the angles in the diagram is 360° , the number of degrees around the circumference of a circle.

If two sides are equal, base angles are equal. Thus a 70° .

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53.

In general:

(A)

q r m p rs n (Note: Figure is not drawn to scale.) If base angles are equal, then sides are equal, so x 3 . 54.

(B)

(Note: Figure is not drawn to scale.) 56.

(B) The greater angle lies opposite the greater side and vice versa. If B A, b a

(Note: Figure is not drawn to scale.) The sum of two sides must be greater than the third side. Try choices: (A) 1 3 4: (A) is not possible (B) 3 4 6; 6 3 4; 4 6 3 . . . O.K. (C) 3 4 10. (C) is not possible (D) 4 3 7. (D) is not possible 55.

57.

(C) The greater side lies opposite the greater angle and vice versa. If b a then B A

(B) Using similar triangles, write a proportion.

58.

(B) Sum of angles of triangle 180°. So 40 60 x 180.

(Note: Figure is not drawn to scale.) x 12 20 15 15x 12 20 12 20 x 15 4 4 12 20 x 16 15 5

100 x 180 x 80

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59.

(C)

61.

(Note: Figure is not drawn to scale.) C. Call it y. First calculate ’s 180°) 80 50 y 180 (Sum of

(B)

In right , a2 b2 c2 So for

y 50 Since C y 50 and B 50, side AB side AC. AB x 4 60.

(C) x° 20° 40° (sum of remote interior angles exterior angle). x 60

52 122 x2 25 144 x2 169 x2 169 x 13 x Note: Specific right triangles you should memorize; use multiples to generate other triangles. Example of multiple:

In general,

zxy

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Memorize the following standard triangles:

62.

(B) Perimeter sum of sides 10 17 21 48

63.

(D) Area of 1/2hb Area of 1/2(8)(21) 84

64.

(A) Area of any triangle 1/2 base height

Here 4 is base and 3 is height. So area /2(4 3) 1/2(12) 6 .

1

65.

(B)

To find perimeter, we need to find the sum of the sides. The sum of the sides is 3 4 x. We need to find x. From the solution in Question 61, we should realize that we have a 3-4-5 right triangle, so x 5. The perimeter is then 3 4 5 12 . Note that you could have found x by using the Pythagorean Theorem: x; 5 x. 32 42 x2; 9 16 x2; 25 x2; 25

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J. Circles 66.

70.

(B) Area pr 2 p(7)2 49p

67.

(C) The diameter cuts a 180° arc on circle, so an inscribed angle y 1/2 arc 1/2 (180°) 90° . Here is a good thing to remember: Any inscribed angle whose triangle base is a diameter is 90°.

(A) Circumference 2p r 2p(7) 14p

K. Other Figures 68.

(B) Inscribed angle 1/2 arc 1 x° 70° 2 35° 71.

(C) Area of parallelogram base height (10)(4) 40

72.

(B) Perimeter sum of sides 5 5 10 10 30

69.

(A) Central angle arc 30° x° Note: The total number of degrees around the circumference is 360°. So a central angle of 30° like 30 1 the one above, cuts the circumference. 360 12

ABCD is a rectangle 73.

(B) In a rectangle (as in a parallelogram) opposite sides are equal. So AD BC 6 .

74.

(C) In a rectangle (as in a parallelogram) opposite sides are equal. So DC AB 8 .

75.

(D) In a rectangle (but not in a parallelogram) the diagonals are equal. So DB AC 10 .

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L. Number Lines

rectangle length width

76.

(B) Area of 4 10 40 .

77.

(B) Perimeter sum of sides

81.

(C) b is between 0 and 1 so 1 b 0

82.

(B) a is between 2 and 1 so 1 a 2

4 4 10 10 28 .

M. Coordinates

78.

(A) Area of square with side x is x2. (All sides of a square are equal.) So length width. Since x 3, x2 9 .

79.

(B) Perimeter of square is the sum of all sides of square. Since all sides are equal, if one side is x, perimeter 4x.

Horizontal right Horizontal left Vertical up Vertical down

x 3, so 4x 12 . 80.

(B) VOLUME OF RECTANGULAR SOLID shown below a b c

83.

(D) a,b,c,h positive (4 letters)

84.

(D) d,e, f,g negative (4 letters)

85.

(C)

So for:

a 8, b 4, c 2 and a b c 8 4 2 64 . Note: VOLUME OF CUBE shown below a a a a3

Remember 3-4-5 right triangle. x 5 You can also use the Pythagorean Theorem: 32 42 x2; 9 16 x2; x2 25; x 5

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N. Inequalities 86.

(A) You can multiply an inequality by a positive number and retain the same inequality: xy 4x 4y

87.

P. Shortcuts 94.

Don’t get a common denominator if you can do something more easily: 7 16

ALWAYS

3 7

MULTIPLY MULTIPLY

49

(A) You can subtract the same number from both sides of an inequality and retain the same inequality: xyz

48

49

48 3 7

7 16

so

xyxzx yzx 88.

ALWAYS

95.

(A) If you multiply an inequality by a minus sign, you reverse the original inequality sign: 4 x

(A) 7 12

MULTIPLY

MULTIPLY

3 7 5 3 12 5 12 5

( 4 x) 4 x 89.

90.

(B) If m n, qm qn if q is positive qm qn if q is negative qm qn if q is zero SOMETIMES So, qm qn

96.

MULTIPLY

MULTIPLY

3 7 5 3 12 5 12 5

ALWAYS

(B) You can’t always multiply inequality relations to get the same inequality relation. For example: 32 2 3

32 21

6 6

62

O. Averages

93.

(A) 7 12

However, if x, y, p, q are positive, then if x y and p q, xp yq.

92.

(A) You can always add inequality relations: xy pq xpyq

91.

ALWAYS

(C) Average of 30 40 80 30 40 80 50 3 Average of x y z t . . . x y z t . . . number of terms TOTAL DISTANCE (B) Average speed TOTAL TIME Distance 40 miles, Time 4 hours 40 miles 10 miles per hour Average speed 4 hours

35 36 60 11 71 1 60 60

97.

35 36 60 1 60

(A) Don’t divide by 250! Multiply both numerator and denominator by 4: 16 4 4 0.016 250 4 1,000

98.

(A) Get rid of denominators! abc 200 2

1

Multiply 1 by 2: 200 2 a b c ab 80 3 Multiply 3 by 3: 80 3 a b

2 3

4

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Now subtract 4 from 2 : 200 2 80 3 a b c (a b) b c a b a 400 240 c 160 c 99.

(D) Don’t multiply 95 75 or 95 74 ! Factor common 95: 95 75 95 74 95(75 74) 95(1) 95

100.

140 15 (C) 57 Don’t multiply 140 15 if you can first reduce. 20 140 15 20 15 5 7 5 1 Further reduce: 3 20 15 60 5 1

101.

(A) You’d be crazy to multiply 70 21 36 4 ! You also cannot approximate because the choices are so close. So look at the product: 70 21 36 4 Since 70 ends in “0,” the product 70 21 36 4 must end in 0! The only choice that ends in 0 is Choice A: 211680 .

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PA R T 4

STRATEGY SECTION Using Critical Thinking Skills to Score High on the SAT

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60 • STRATEGY SECTION

5 General Strategies

General Strategies for Taking the SAT Examination Before studying the 35 specific strategies for the Math and Critical Reading questions, you will find it useful to review the following 5 General Strategies for taking the SAT examination.

Strategy 1: DON’T RUSH INTO GETTING AN ANSWER WITHOUT THINKING. BE CAREFUL IF YOUR ANSWER COMES TOO EASILY, ESPECIALLY IF THE QUESTION IS TOWARD THE END OF THE SECTION.

Beware of Choice A If You Get the Answer Fast or Without Really Thinking Everybody panics when they take an exam like the SAT. And what happens is that they rush into getting answers. That’s OK, except that you have to think carefully. If a problem looks too easy, beware! And, especially beware of the Choice A answer. It’s usually a “lure” choice for those who rush into getting an answer without critically thinking about it. Here’s an example:

that the test maker would give you such an easy question? The fact that you figured it out so easily and saw that Choice A was your answer should make you think twice. The thing you have to realize is that there is another possibility: 12:12 to 1:01 gives 49 minutes, and so Choice E is correct. So, in summary, if you get the answer fast and without doing much thinking, and it’s a Choice A answer, think again. You may have fallen for the Choice A lure. NOTE: Choice A is often a “lure choice” for those who quickly get an answer without doing any real thinking. However, you should certainly realize that Choice A answers can occur, especially if there is no “lure choice.”

Strategy 2: KNOW AND LEARN THE DIRECTIONS TO THE QUESTION

Below is a picture of a digital clock. The clock shows that the time is 6:06. Consider all the times on the clock where the hour digit is the same as the minute digit like in the clock shown below. Another such “double” time would be 8:08 or 9:09. What is the smallest time period between any two such doubles?

TYPES BEFORE YOU TAKE THE ACTUAL TEST.

(A) 61 minutes (B) 60 minutes (C) 58 minutes (D) 50 minutes (E) 49 minutes

All SATs are standardized. For example, all the Analogy questions have the same directions from test to test as do the Sentence Completions, etc. So it’s a good idea to learn these sets of directions and familiarize yourself with their types of questions early in the game before you take your actual SAT. Here’s an example of a set of SAT directions, together with an accompanying example for the Sentence Completion type of questions.

6:06

Did you subtract 7:07 from 8:08 and get 1 hour and 1 minute (61 minutes)? If you did you probably chose Choice A: the lure choice. Think—do you really believe

Never Spend Time Reading Directions During the Test or Doing Sample Questions That Don’t Count

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STRATEGY SECTION • 61

For each question in this section, select the best answer from among the choices given and fill in the corresponding oval on the answer sheet.

Directions: Each sentence below has one or two blanks, each blank indicating that something has been omitted. Beneath the sentence are five words or set of words labeled A through E. Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. Example: Medieval kingdoms did not become constitutional republics overnight; on the contrary, the change was____.

have at least a chance of getting the question right. Suppose, for example, that you have a five-choice question:

From a probablistic point of view, it is very likely that you would get one question right and four wrong (you have a 1 in 5 chance of getting a five-choice question right) if you randomly guess at the answers. Since 1 /4 point is taken off for each wrong five-choice question, you’ve gotten 1 1⁄4 4 0 points, because you’ve gotten 1 question right and 4 wrong. Thus you break even. So the moral is whether you randomly guess at questions you’re not sure of at all or whether you leave those question answers blank, it doesn’t make a difference in the long run!

Strategy 4: WRITE AS MUCH AS YOU WANT IN YOUR TEST BOOKLET.

(A) (B) (C) (D) (E)

unpopular unexpected advantageous sufficient gradual

Test Booklets Aren’t Graded—So Use Them As You Would Scrap Paper ABCD

If on your actual test you spend time reading these directions and/or answering the sample question, you will waste valuable time. As you go through this book, you will become familiar with all the question types so that you won’t have to read their directions on the actual test.

Strategy 3: IT MAY BE WISER NOT TO LEAVE AN ANSWER BLANK.

The Penalty for Guessing Is Much Smaller Than You Might Expect On the SAT you lose a percentage of points if you guess and get the wrong answer. Of course, you should always try to eliminate choices. You’ll find that, after going through this book, you’ll have a better chance of eliminating wrong answers, However, if you cannot eliminate any choice in a question and have no idea of how to arrive at an answer, you might want to pick any answer and go on to the next question. There are two reasons for this: 1. You don’t want to risk mismarking a future answer by leaving a previous answer blank. 2. Even though there is a penalty for guessing, the penalty is much smaller than you might expect, and this way you

Many students are afraid to mark up their test booklets. But, the booklets are not graded! Make any marks you want. In fact, some of the strategies demand that you extend or draw lines in geometry questions or label diagrams, or circle incorrect answers, etc. That’s why when I see computer programs that show only the questions on a screen and prevent the student from marking a diagram or circling an answer, I realize that such programs prevent the student from using many powerful strategies. So write all you want on your test booklet—use your test paper as you would scrap paper.

Strategy 5: USE YOUR OWN CODING SYSTEM TO TELL YOU WHICH QUESTIONS TO RETURN TO.

If You Have Extra Time After Completing a Test Section, You’ll Know Exactly Which Questions Need More Attention When you are sure that you have answered a question correctly, mark your question paper with ✓. For questions you are not sure of but for which you have eliminated some of the choices, use ?. For questions that you’re not sure of at all or for which you have not been able to eliminate any choices, use ??. This will give you a bird’s-eye view of what questions you should return to, if you have time left after completing a particular test section.

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35 Easy-to-Learn Strategies 19 Math Strategies 16 Verbal (Critical Reading) Strategies Critical thinking is the ability to think clearly in order to solve problems and answer questions of all types—SAT questions, for example, both Math and Verbal! Educators who are deeply involved in research on Critical Thinking Skills tell us that such skills are straightforward, practical, teachable, and learnable. The 19 Math Strategies and 16 Verbal Strategies in this section are Critical Thinking Skills. These strategies have the potential to raise your SAT scores dramatically. A realistic estimate is anywhere from approximately 50 points to 300 points in each part of the test—Critical Reading and Math. Since each correct SAT question gives you an additional 10 points on average, it is reasonable to assume that if you can learn and then use these valuable SAT strategies, you can boost your SAT scores phenomenally! BE SURE TO LEARN AND USE THE STRATEGIES THAT FOLLOW!

How to Learn the Strategies 1. For each strategy, look at the heading describing the strategy. 2. Try to answer the first example without looking at the EXPLANATORY ANSWER. 3. Then look at the EXPLANATORY ANSWER and if you got the right answer, see if the method described would enable you to solve the question in a better way with a faster approach. 4. Then try each of the next EXAMPLES without looking at the EXPLANATORY ANSWERS. 5. Use the same procedure as in (3) for each of the EXAMPLES. The MATH STRATEGIES start on page 69, and the VERBAL STRATEGIES start on page 117. However, before you start the Math Strategies, it would be wise for you to look at the Important Note on the Allowed Use of Calculators on the SAT following; The Important Note on Math Questions on the SAT, page 63; The Grid-Type Question, page 63; and Use of a Calculator in the Grid-Type Question, page 67.

Important Note on the Allowed Use of Calculators on the SAT Although the use of calculators on the SAT I will be allowed, using a calculator may be sometimes more tedious, when in fact you can use another problemsolving method or shortcut. So you must be selective on when and when not to use a calculator on the test. Here’s an example of when a calculator should not be used: 2 5 6 7 8 10 9 5 6 7 8 9 11 10 9 (A) 11

2 (B) 11

11 (C) 36

10 (D) 21

244 (E) 360

Here the use of a calculator may take some time. However, if you use the strategy of canceling numerators and denominators (Math Strategy 1 on pages 69–70) as shown:

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Cancel numerators/denominators: 9 2 5 6 7 8 10 2 5 6 7 8 9 11 10 11 2 You can see that the answer comes easily as . 11 Later I will show you an example in the grid-type question where the use of a calculator will also take you a longer time to solve a problem than without the calculator. Here’s an example where using a calculator may get you the solution as fast as using a strategy without the calculator: 1

25 percent of 16 is equivalent to ⁄2 of what number? (A) 2 (B) 4 (C) 8 (D) 16 (E) 32 Using a calculator, you’d use Math Strategy 2 (page 71) (translating of to times and is to equals), first calculating 25 percent of 16 to get 4. Then you’d say 4 half of what number and you’d find that number to be 8. Without using a calculator, you’d still use Math Strategy 2 (the translation strategy), but you could write 25 percent as 1⁄4 , so you’d figure out that 1⁄4 16 was (4). Then you’d call the number you want to find x, and say 4 1⁄2(x). You’d find x 8. Note that both methods, with and without a calculator, are about equally efficient; however, the technique in the second method can be used for many more problems and hones more thinking skills.

Important Note on Math Questions on the SAT There are two types of math questions on the SAT. 1. The Regular Math (total of 44 counted questions), which has five choices. The strategies for these start on page 69. 2. The “Grid-Type” Math Question (total of 10 counted questions) is described below. Note: The grid-type questions can be solved using the Regular Math Strategies.

The Grid-Type Math Question There will be 10 questions on the SAT I where you will have to “grid” in your answer rather than choose from a set of five choices. Here are the directions to the “gridtype” question. Make sure that you understand these directions completely before you answer any of the gridtype questions.

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Directions: For Student-Produced Response questions 9–18, use the grids at the bottom of the answer sheet page on which you have answered questions 1–8. Each of the remaining 10 questions requires you to solve the problem and enter your answer by marking the circles in the special grid, as shown in the examples below. You may use any available space for scratchwork. 7 Answer: ᎏ or 7/12 12

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Note: You may start your answers in any column, space permitting. Columns not needed should be left blank.

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Mark no more than one oval in any column.

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Because the answer sheet will be machinescored, you will receive credit only if the ovals are filled in correctly.

Decimal Accuracy: If you obtain a decimal answer, enter the most accurate value the grid will accommodate. For example, if you obtain an answer such as 0.6666 … , you should record the result as .666 or .667. Less accurate values such as .66 or .67 are not acceptable.

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2 Acceptable ways to grid ᎏ ⫽ .6666 … 3

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Some problems may have more than one correct answer. In such cases, grid only one answer.

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Practice with Grids According to the directions on the previous page, grid the following values in the grids 1–15:

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Use of a Calculator in the Grid-Type Question In the following example, you can either use a calculator or not. However, the use of a calculator will require a different gridding. EXAMPLE:

2 3 If x find one value of x. 7 7 SOLUTION WITHOUT A CALCULATOR:

4 2 3 2 Get some value between and . Write and 14 7 7 7 6 3 . 14 7 4 6 5 So we have x and x can be . 14 14 14 The grid will look like:

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68 • STRATEGY SECTION SOLUTION WITH A CALCULATOR:

Calculate on calculator: 3 .4285714 . . . 7 2 .2857142 . . . 7 So .2857142 x .4285714. You could have the grid as follows: .

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19 Math Strategies

Using Critical Thinking Skills in Math Questions

MATH GY STRATE

Cancel Quantities to Make the Problem Simpler Cancel numbers or expressions that appear on both sides of an equation; cancel same numerators and denominators. But make sure that you don’t divide by 0 in what you’re doing! You will save precious time by using this strategy. You won’t have to make any long calculations. EXAMPLE 1

11 11 8 If P , then P 14 14 9 8 (A) 9 9 (B) 8 (C) 8 (D) 11 (E) 14 11 8 Choice A is correct. Do not multiply ! 9 14 11 Cancel the common : 14 11 11 8 P 14 14 9 8 P ( Answer) 9 11 Note: You can cancel the because you are dividing 14 both sides by the same nonzero number. Suppose you had a problem like the following:

4 If R a a , then R 5

2 (A) 3 4 (B) 5 (C) 1 5 (D) 4 (E) Cannot be determined. What do you think the answer is? It’s not Choice A! It is Choice E because you cannot cancel the “a” because a may be 0 and you cannot divide by 0. So if a 0, R can be any number. EXAMPLE 2

7 6 3 7 6 If y , then y 5 13 19 13 19 6 (A) 19 13 (B) 32 7 (C) 13 3 (D) 5 211 (E) 247 Choice D is correct. Do not add the fractions!

1

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3 7 6 ! You will waste a lot of time! There is a 5 13 19 7 6 much shorter way to do the problem. Cancel 13 19 from both sides of the equation. Thus,

3 7 6 7 6 y 5 13 19 13 19 3 y ( Answer) 5

EXAMPLE 5

y 2 If 7 6 , y 9 27 (A) (B) (C) (D) (E)

8 30 35 37 33

EXAMPLE 3

Choice E is correct. 2 5 6 7 8 10 9 5 6 7 8 9 11 10 9 (A) 11 2 (B) 11 11 (C) 36 10 (D) 21 244 (E) 360 Choice B is correct. C an celn u m erato rs/ d en o m in ato rs: 2 5 6 7 8 9 2 10 5 6 7 8 9 10 11 11 EXAMPLE 4

If a b a b, which must follow? (A) (B) (C) (D) (E)

a 0 b 0 ab ba b0

Choice E is correct. abab Can celco m m o n a ’s: b a ab bb Add b: b b b b 2b 0 b0

S btract 6 from both sides: u y 2 7 6 6 6 9 27 y 2 1 9 27 y 11 9 27 y 33 27 27 y 33

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MATH GY STRATE

Translate English Words into Mathematical Expressions

Many of the SAT problems are word problems. Being able to translate word problems from English into mathematical expressions or equations will help you to score high on the test. The following table translates some commonly used words into their mathematical equivalents:

TRANSLATION TABLE Words is, as, was, has, cost of percent x percent which, what

Math Way to Say It (equals) (times) /100 (the percent number over 100) x/100 x (or any other variable)

x and y the sum of x and y the difference between x and y x more than y x less than y the product of x and y the square of x x is greater than y x is less than y

xy xy xy xy yx xy x2 x y (or y x) x y (or y x)

y years ago y years from now c times as old as John x older than y x younger than y

y y c ( John’s age) xy yx

the increase from x to y the decrease from x to y

yx xy yx 100 x

the percent increase from x to y ( y x)

the percent decrease from x to y ( y x)

x 100

xy

the percent of increase

100 original amount

the percent of decrease

100 original amount

n percent greater than x

n x x 100

n percent less than x

n x x 100

amount of increase

amount of decrease

By knowing this table, you will find word problems much easier to do.

2

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OPTIONAL QUIZ ON TRANSLATION TABLE Take this quiz to see if you understand the translation table before attempting the problems in Strategy #2 that follow.

1.

Mar y is five years older than John translates to: (A) (B) (C) (D) (E)

1.

2.

(D) Six years ago, Sarah was translates to S 6 4 times as old as John is would be 4J. However, 4 times as old as John was then translates to 4(J 6). Thus Six years ago, Sarah was 4 times as old as John was then translates to: S 6 4 (J 6)

5.

The percent increase from 5 to 10 is

J5M MJ5 M5J M5J None of these.

(D) Translate: Mar y to M; John to J; is to ; older than to So Mar y is five years older than John becomes:

↓ ↓ ↓

↓

↓

M 5

J

(A) (B) (C) (D) (E)

3 percent of 5 translates to: (A) (B) (C) (D) (E)

2.

4.

3/5 3/100 divided by 5 (3/100) 5 3 100 5 None of these.

5.

(A) Percent increase from a to b is [(b a)/a] 100. So the percent increase from 5 to 10 would be [(10 5)/5] 100.

6.

Harr y is older than John and John is older than Mar y translates to:

(C) percent or % /100; of ; so

(A) (B) (C) (D) (E)

3% of 5 translates to: 3/100 5 3.

What percent of 3 translates to: (A) x(100) 3 (B) (x/100) 3 (C) (x/100) divided by 3 (D) (3/100)x (E) None of these.

3.

(A) Harr y is older than John translates to: H J. John is older than Mary translates to J M. So we have H J and J M which consolidated becomes: H J M.

7.

Even after Phil gives Sam 6 compact discs, he still has 16 more compact discs than Sam has translates to:

What percent of 3 becomes: x 4.

↓ /100

↓↓

(A) (B) (C) (D) (E)

3

Six years ago, Sarah was 4 times as old as John was then translates to: (A) (B) (C) (D) (E)

S 6 4J 6 S 4J 6 S 4(J 6) S 6 4(J 6) None of these.

HJM HJ M HMJ MHJ None of these.

6.

(B) Translate: what to x; percent to /100. Thus

↓

[(10 5)/5] 100 [(5 10)/5] 100 [(10 5)/10] 100 [(5 10)/10] 100 None of these.

7.

P 6 16 S P 6 16 S 6 P 6 16 S 6 P 6 16 S None of these.

(B) (1) Even after Phil gives Sam 6 compact discs translates to: P6 (2) He still has 16 more compact discs than Sam has translates to: 16 S 6 since Sam has gotten 6 additional compact discs. Thus combining (1) and (2), we get: P 6 16 S 6.

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STRATEGY SECTION • 73 8.

q is 10% greater than p translates to: (A) (B) (C) (D) (E)

8.

q (10/100)q p q (10/100)p q (10/100)p p q (10/100) p None of these.

(C) (1) q is translates to q (2) 10% greater than p translates to (10/100)p p so q is 0% greater than p translates to:

↓↓ q (10/100)p p

9.

200 is what percent of 20 translates to: (A) (B) (C) (D) (E)

200 x 100 20 200 (x /100) divided by 20 200 (x /100) 20 200 x 20 None of these.

9.

(C) Translate is to ; what to x; percent to /100, of to so we get that: 200 is what percent of 20 translates to: 200 x /100 20

10. The product of the sums of x and y and y and z

is 5 translates to: (A) (B) (C) (D) (E)

xy yz 5 xyyz5 (x y)( yz) 5 (x y)( y z) 5 None of these.

10. (D) The sum of x and y is x y. The sum of y z

is y z. So the product of those sums is (x y) ( y z). Thus The product of the sums of x and y and y and z is 5 translates to: (x y)( y z) 5

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EXAMPLE 1

EXAMPLE 3

Sarah is twice as old as John. Six years ago, Sarah was 4 times as old as John was then. How old is John now? (A) (B) (C) (D) (E)

3 9 18 20 impossible to determine

Choice B is correct. Translate:

“If A is 250 percent of B” becomes ↓↓ ↓ ↓ ↓ ↓ A 250 /100 B

S 2J

1

Six years ago Sarah was 4 times as old as John was then

↓ ↓ ↓

6

S

4

↓

↓

(A) 125% 1 (B) % 250 (C) 50% (D) 40% (E) 400% Choice D is correct.

Sarah is twice as old as John. ↓ ↓ ↓ ↓ ↓ S 2 J

↓

If A is 250 percent of B, what percent of A is B?

( J 6)

This becomes S 6 4( J 6)

“What percent of A is B?” becomes ↓ ↓ ↓↓↓↓ x /100 A B Set up the equations:

2

250 A B 100

Substituting 1 into 2 : 2J 6 4( J 6) 2J 6 4J 24 18 2J 9J ( Answer)

x A B 100

Choice D is correct. Translate: 200 is what percent of 20 ↓ ↓ ↓ ↓ ↓ ↓ 200 x 20 100 x 200 (20) 100 x Divide by 20: 10 100 Multiply by 100: 1,000 x ( Answer)

2

Divide equation 1 by equation 2 : 250 A B 100 x A B 100

EXAMPLE 2

200 is what percent of 20? 1 (A) 10 (B) 10 (C) 100 (D) 1,000 (E) 10,000

1

We get: 1 250 100 Inverting, we get: 100 x 250 100 10,000 x 250 To simplify, multiply both numerator and denominator by 4: 10,000 4 x 40 250 4

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Alternate way:

EXAMPLE 5

Let B ⫽ 100 (choose any number for B). We get (after translation)

冢冣

250 A ⫽ ᎏᎏ 100 100

冢ᎏ10ᎏ0 冣 A ⫽ 100 x

1 2

From 1 , A ⫽ 250 Substituting 3 into 2 , we get

3

冢ᎏ10ᎏ0 冣 250 ⫽ 100 x

Phil has three times as many DVDs as Sam has. Even after Phil gives Sam 6 DVDs, he still has 16 more DVDs than Sam has. What was the original number of DVDs that Phil had? (A) (B) (C) (D) (E)

20 24 28 33 42

Choice E is correct.

Multiplying both sides of 4 by 100, (x)(250) ⫽ (100)(100) Dividing by 250:

Phil has three times as many DVDs as Sam has ↓ ↓ ↓ ↓ ↓ P ⫽ 3 ⫻ S Even after Phil gives Sam 6 DVDs, he still has 16 ↓ ↓ ↓ ↓ ↓ P ⫺ 6 ⫽ 16

再

100 ⫻ 100 x ⫽ ᎏᎏ 250

Translate:

100 ⫻ 100 ⫻ 4 40,000 x ⫽ ᎏᎏ ⫽ ᎏᎏ 250 ⫻ 4 1,000 ⫽ 40 EXAMPLE 4

more DVDs than Sam has ↓ ↓ ⫹ S⫹6

再

Simplify by multiplying numerator and denominator by 4:

Sam now has S ⫹ 6 DVDs because Phil gave Sam 6 DVDs. So we end up with the equations: P ⫽ 3S

John is now m years old and Sally is 4 years older than John. Which represents Sally’s age 6 years ago? (A) (B) (C) (D) (E)

P ⫺ 6 ⫽ 16 ⫹ S ⫹ 6 Find P ; get rid of S:

m ⫹ 10 m ⫺ 10 m⫺2 m⫺4 4m ⫺ 6

P ⫽ 3S;

P P ⫺ 6 ⫽ 16 ⫹ ᎏᎏ ⫹ 6 3 48 ⫹ P ⫹ 18 P ⫺ 6 ⫽ ᎏᎏ 3

Choice C is correct. Translate: John is now m years old ↓ ↓ ↓ J ⫽ m

3P ⫺ 18 ⫽ 48 ⫹ P ⫹ 18 2P ⫽ 84 P ⫽ 42

Sally is 4 years older than John ↓ ↓ ↓ ↓ ↓ S ⫽4 ⫹ J Sally’s age 6 years ago ⫽ ↓ ↓ S ⫺ 6 ⫽ So we get:

J⫽m S⫽4⫹J

and find: S ⫺ 6 ⫽ 4 ⫹ J ⫺ 6 S ⫺ 6 ⫽ J ⫺ 2 (substituting m for J ) S⫺6⫽m⫺2

P ᎏᎏ ⫽ S 3

EXAMPLE 6

If q is 10 % greater than p and r is 10% greater than y, qr is what percent greater than py? (A) (B) (C) (D) (E)

1% 20% 21% 30% 100%

Choice C is correct.

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Translate:

Then: qr 11 22 and py 20 10 So, to find what percent qr is greater than py, you would need to find:

If q is 10% greater than p

↓↓

↓

10 p p 100

q

and r is 10% greater than y

↓↓

qr py 100 or py 11 22 20 10 100 20 10

↓

10 y y 100 qr is what percent greater than py?

r

↓ ↓

↓

This is:

x py py 100

qr

42 100 21 200

So we have three equations:

10 10 q p p 1 p 100 100 10 10 r y y 1 y 100 100 x x qr py py 1 py 100 100

EXAMPLE 7

1 Sales of Item X Jan–June, 2004 Month Sales ($) Jan 800 Feb 1,000 Mar 1,200 Apr 1,300 May 1,600 Jun 1,800

2 3

Multiply 1 and 2 : 2 10 qr 1 py 100

4

Now equate 4 with 3 : 2 x 10 qr 1 py 1 py 100 100

2

2

10 You can see that 1 100

x 1, canceling py. 100

1 2 1 10,000 100 100

10 So, 1 100

100

10

x

100 20 21 x 10,000 100 100 100 The answer is x 21.

21 x

Alternate approach: Choose numbers for p and for y: Let p 10 and y 20 Then, since q is 10% greater than p:

According to the above table, the percent increase in sales was greatest for which of the following periods? (A) (B) (C) (D) (E)

Jan–Feb Feb–Mar Mar–Apr Apr–May May–Jun

Choice A is correct. The percent increase from Month A to Month B Sales (Month B) Sales (Month A) 100 Sales (Month A) Month Sales ($) Jan

800 Jan– 1,000 800 200 100 100 Feb 800 800

Feb 1,000

q 10% greater than 10

10 q 10 10 11 100 Next, r is 10% greater than y :

Feb– Mar

Mar 1,200 Mar– Apr Apr 1,300

r 10% greater than 20 10 Or, r 20 20 22 100

% Increase in Sales

Apr– May

1,200 1,000 2 00 100 100 1, 000 1,000 1,300 1,200 1 00 100 100 1,200 1,200 1,600 1,300 3 00 100 100 1, 300 1,300

May 1,600 May–

1,800 1,600 200 100 100 Jun 1,6 00 1,600

Jun 1,800 200 You can see that 100 (Jan–Feb) is the greatest. 800

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MATH GY T S RATE

Know How to Find Unknown Quantities (Areas, Lengths, Arc and Angle Measurements) from Known Quantities (the Whole Equals the Sum of Its Parts) When Asked to Find a Particular Area or Length, Instead of Trying to Calculate It Directly, Find It by Subtracting Two Other Areas or Lengths—a Method Based on the Fact That the Whole Minus a Part Equals the Remaining Part

EXAMPLE 2

E is a straight line, and F is a In the diagram below, A . Find an expression for m DFE. point on AE

This strategy is very helpful in many types of geometry problems. A very important equation to remember is The whole the sum of its parts

1

Equation 1 is often disguised in many forms, as seen in the following examples: EXAMPLE 1

(A) (B) (C) (D) (E)

x y 60 x y 60 90 x y 120 x y 180 x y

Choice D is correct. Use equation 1 . Here, the whole refers to the straight angle, AFE, and its parts refer to AFB, BFC, CFD, and DFE. Thus,

In the diagram above, XYZ has been inscribed in a circle. If the circle encloses an area of 64, and the area of XYZ is 15, then what is the area of the shaded region? (A) (B) (C) (D) (E)

25 36 49 79 It cannot be determined from the information given.

or

mAFE m AFB mBFC mCFD mDFE 180 x 60 y mDFE mDFE 180 x 60 y mDFE 120 x y (Answer) EXAMPLE 3

In the diagram below, AB m, BC n, and AD 10. Find an expression for CD. (Note: Diagram represents a straight line.)

Choice C is correct. Use equation 1 . Here, the whole refers to the area within the circle, and the parts refer to the areas of the shaded region and the triangle. Thus, Area within circle Area of shaded region Area of XYZ 64 Area of shaded region 15 or Area of shaded region 64 15 49 ( Answer)

(A) (B) (C) (D) (E)

10 mn 10 m n m n 10 m n 10 m n 10

3

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Choice B is correct. Use equation 1 . Here, the whole refers to AD, and its parts refer to AB, BC, and CD. Thus,

or

AD AB BC CD 10 m n CD CD 10 m n ( Answer) EXAMPLE 4

The area of triangle ACE 64. The sum of the areas of the shaded triangles ABF and FDE is 39. What is the side of square BFDC?

p (B) 9 1 2

p 1 (A) 9 4 2

(C) 9(p 1)

p 1 (D) 9 4 4

(E) Cannot be determined. EXPLANATORY ANSWER

Choice A is correct. S u b tractk n o w n sfro m k n o w n s: Area of shaded region area of quarter circle AOB area of triangle AOB (A) (B) (C) (D) (E)


p(3)2 Area of quarter circle AOB 4 33 Area of triangle AOB (since OB 3 and 2 1 area of a triangle base height) 2

EXPLANATORY ANSWER

9p 9 p 1 Thus, area of shaded region 9 . 4 2 4 2

Choice A is correct. Since we are dealing with areas, let’s establish the area of the square BFDC, which will then enable us to get its side.

EXAMPLE 6

Now, the area of square BFDC area of triangle ACE (area of triangles ABF FDE) Area of square BFDC 64 39 25 Therefore, the side of square BFDC 5. EXAMPLE 5

The sides in the square above are each divided into five equal segments. What is the value of Area of square ? Area of shaded region

In the figure above, O is the center of the circle. Triangle AOB has side 3 and angle AOB 90°. What is the area of the shaded region?

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50 (A) 29

EXAMPLE 7

50 (B) 21 25 (C) 4 29 (D) 25 (E) None of these. EXPLANATORY ANSWER

Choice B is correct.

Two concentric circles are shown above with inner radius of m and outer radius of n. What is the area of the shaded region? (A) (B) (C) (D) (E)

p(n m)2 p(n2 m2) p(n2 m2) 2p(n m) 2p(n m) EXPLANATORY ANSWER

Choice C is correct. Subtract knowns from knowns: Subtract knowns from knowns: Area of square 5 5 25 Area of shaded region area of square area of I area of II area of III area of IV 33 9 Area of I 2 2 21 Area of II 1 2 44 Area of III 8 2 21 Area of IV 1 2 9 21 Area of shaded region 25 1 8 1 2 2 25 Area of square 2 50 25 21 Area of shaded region 21 21 2

Area of shaded region area of circle of radius n area of circle of radius m Area of circle of radius n pn 2 Area of circle of radius m pm 2 Area of shaded region pn 2 pm 2 p(n 2 m 2)

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MATH GY T S RATE

Remember Classic Expressions Such as

x y x 2 y 2, x 2 2x y y 2, x 2 2x y y 2, xy

Memorize the following factorizations and expressions: x y (x y) (x y)

Equation 1

x2 2xy y2 (x y) (x y) (x y)2 x2 2xy y2 (x y)(x y) (x y)2 xy 1 1 x, y 0 xy x y xy 1 1 x, y 0 xy y x xy xz x(y z)

Equation 2

2

2

xy xz x(y z)

Now substitute the numbers 34 and 66 back into 1 to get: 662 2(34)(66) 342 (66 34)(66 34) 100 100

Equation 3 Equation 4

10,000

( Answer)

Equation 4A EXAMPLE 2

Equation 5 Equation 5A

Examples 1, 3, 4, and 9 can also be solved with the aid of a calculator and some with the aid of a calculator allowing for exponential calculations. However, to illustrate the effectiveness of Math Strategy 4, we did not use the calculator method of solution of these examples.

1 1 If (x y) 9 and xy 14, find . x y (Note: x, y 0) 1 (A) 9

2 (B) 7

9 (C) 14

(D) 5 (E) 9

Choice C is correct. We are given: (x y) 9 xy 14 x, y 0

Use algebra to see patterns.

1 2 3

EXAMPLE 1

I hope that you did not solve 2 for x (or y), and then substitute it into 1 . If you did, you obtained a quadratic equation.

66 2(34)(66) 34 2

(A) (B) (C) (D) (E)

2

4,730 5,000 9,860 9,950 10,000

Here is the FAST method. Use Equation 4: 1 1 xy x y xy

Choice E is correct. Notice that there is a 34 and 66 running through the left side of the equality. To see a pattern, use algebra. Substitute a for 66 and b for 34. You get: 662 2(34)(66) 342 a2 2(b)(a) b2 But from Equation 2, a2 2ab b2 (a b)(a b) (a b)2

1

From 1 and 2 , we find that 4 becomes 1 1 9 ( Answer) x y 14

4

4

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EXAMPLE 3

EXAMPLE 6

The value of 100 100 99 99

If a b 4 and a b 7, then a2 b2

(A) (B) (C) (D) (E)

(A) (B) (C) (D) (E)

l 2 99 199 299

Choice D is correct. Write a for 100 and b for 99 to see a pattern: 100 100 99 99 a a b b a2 b2. Use Equation 1: Use the fact that a2 b2 (a b)(a b) 1 Put back 100 for a and 99 for b in 1 : a2 b2 1002 992 (100 99)(100 99) 199

Use factoring to make problems simpler.

(Equation 1)

EXAMPLE 7

22 (A) 121 5 (B) 6 21 (C) 110 13 (D) 22 (E) 1

87 8 6 7 (A) 8/7 87 86 85 84

Choice C is correct. Factor: 87 86 86(81 1) 86(8 1) 86(7)

(Equation 5A)

Choice C is correct. xy 1 1 Use xy x y

) 87 86 86(7) 86(7 So 86 7 7 7 EXAMPLE 5

1 1 If y 9, then y 2 2 y y (A) (B) (C) (D) (E)

Choice C is correct. Use (a b)(a b) a2 b2 ab4 ab7 (a b)(a b) 28 a2 b2

xy What is the least possible value of if xy 2 x y 11 and x and y are integers?

EXAMPLE 4

(B) (C) (D) (E)

51/2 11 28 29 56

76 77 78 79 81

(Equation 4)

1 1 is least when x is greatest and y is greatest. x y Since it was given that x and y are integers and that 2 x

y 11, the greatest value of x is 10 and the greatest value of y is 11. 1 1 xy So the least value of x y xy 10 11 21 . 10 11 110 EXAMPLE 8

If (a b)2 20 and ab 3, then a2 b2

Choice D is correct.

1 Square y y

1 1 y 2 81 y 2 2 2 (Equation 2) y y 1 79 y 2 2 y

(A) (B) (C) (D) (E)

14 20 26 32 38


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82 • STRATEGY SECTION 2 2 2 U b se(a b) a 2a b 20

(Use Equation 2)

Use (a b)(a b) a2 b2

(Use Equation 1)

Substitute 2ab 6 in:

Write: 998 1,002 (1,000 2)(1,000 2) 106 x 1,0002 4 106 x (103)2 4 106 x 106 4 106 x

a2 2ab b2 20

Multiply by 1; reverse inequality sign:

ab 3 So, 2ab 6

l(4 x) 4 x

We get: a2 6 b2 20 a2 b2 26

EXAMPLE 10

EXAMPLE 9

If x2 y2 2xy and x 0 and y 0, then If 998 1,002 106 x, x could be (A) (B) (C) (D) (E)

4 but not 3 4 but not 5 5 but not 4 3 but not 4 3, 4, or 5

(A) (B) (C) (D) (E)

x 0 only y 0 only x 1, y 1, only xy0 xy

Choice E is correct. Simplify by subtracting to get form of Equation 3: x 2 2xy y 2 (x y)(x y). That is, subtract 2xy from both sides of given problem equation to get x 2 2xy y 2 0. Thus (x y)(x y) x 2 2xy y 2 0 so x y 0 and thus x y.


MATH GY T S RATE

Know How to Manipulate Averages

Almost all problems involving averages can be solved by remembering that Sum of the individual quantities or measurements Average Number of quantities or

Choice B is correct. Recall that

Sum of the individual measurements

Average Number of measurements Let x height (in inches) of the third student. Thus,

measurements

70 72 x 68 3

(Note: Average is also called Arithmetic Mean.) Multiplying by 3, EXAMPLE 1

The average height of three students is 68 inches. If two of the students have heights of 70 inches and 72 inches respectively, then what is the height (in inches) of the third student? (A) (B) (C) (D) (E)

60 62 64 65 66

204 70 72 x or 204 142 x or x 62 inches (Answer).

5

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EXAMPLE 2

4.

The average of 30 numbers is 65. If one of these numbers is 65, the sum of the remaining numbers is (A) (B) (C) (D) (E)

Scores on five tests range from 0 to 100 inclusive. If Don gets 70 on the first test, 76 on the second, and 75 on the third, what is the minimum score Don may get on the fourth test to average 80 on all five tests? (A) (B) (C) (D) (E)

65 64 30 64 29 30 29 64 29 65


5.

sum of numbers Average 30 Call the numbers a, b, c, d, etc. abcd... So 65 30

Since we were told one of the numbers is 65, let a 65:

6.


The average length of 10 objects is 25 inches. If the average length of 2 of these objects is 20 inches, what is the average length of the remaining 8 objects?

65 30 65 b c d . . . So 65 30 65 b c d . . .

Eighteen students attained an average score of 70 on a test and 12 students on the same test scored an average of 90. What is the average score for all 30 students on the test? (A) (B) (C) (D) (E)

Now immediately get rid of the fractional part: Multiply by 30 to get: 65 30 a b c d . . . .

76 79 82 89 99

sum of remaining numbers Factor: 65 30 65 65 (30 1) sum of remaining numbers 65 29 sum of remaining numbers EXAMPLES 36

3.

The average length of 6 objects is 25 cm. If 5 objects are each 20 cm in length, what is the length of the sixth object in cm? (A) (B) (C) (D) (E)

55 50 45 40 35

(A) 221/2 inches (B) 24 inches (C) 261/4 inches (D) 28 inches (E) Cannot be determined.

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“Twelve students on the same test scored an average of 90” translates to:

EXPLANATORY ANSWERS FOR EXAMPLES 3–6

3.

(B) Use the formula:

Sum of scores of other 12 students 90 12

Sum of individual items Average Number of items

Now what you are looking for is the average score of all 30 students. That is, you are looking for:

Now call the length of the sixth item, x. Then:

Sum of scores of all 30 students Average of 30 students 30

20 20 20 20 20 x 25 6 20 5 x or 25 6

25 6 20 5 x 150 100 x 50 x

Now, the sum of all 30 students sum of scores of 18 students sum of scores of other 12 students. And this can be gotten from 1 and 2 :

(B) Use the formula:

From 1 : 70 18 sum of scores of 18 students

Sum of scores on tests Average Number of tests

From 2 : 90 12 sum of scores of other 12 students

Let x be the score on the fourth test and y be the score on the fifth test.

So adding: 70 18 90 12 sum of scores of 18 students sum of scores of other 12 students sum of scores of 30 students

Then: 70 76 75 x y 80 Average 5

Put all this in 3 : 70 18 .90 12 Average of 30 students 30

The minimum score x Don can get is the lowest score he can get. The higher the score y is, the lower the score x can be. The greatest value of y can be 100. So:

70 18 90 12 30

70 76 75 x 100 80 5

7 18 9 12 3

321 x 80 5

6 3 7 18 9 12 3 42 36 78

Multiply by 5: 400 321 x 79 x 5.

3

So, if you can find the sum of scores of all 30 students, you can find the required average.

Multiply by 6:

4.

2

6.

(A) Use the formula: Sum of scores Average Number of students

sum of 10 lengths

“Eighteen students attained an average of 70 on a test” translates mathematically to: Sum of scores of 18 students 70 18

(C) Denote the lengths of the objects by a, b, c, d, etc. Since the average length of 10 objects is given to be 25 inches, establish an equation for the average length:

1

a b c d ... j Average length 25 10

1

number of objects

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The question also says that the average length of 2 of these objects is 20. Let the lengths of two we choose be a and b. So,

Now, remember, we want to find the value of x: cde...j x 8

lengths of 2 objects

ab Average length of a and b 20 2

2 number of objects

Now we want to find the average length of the remaining objects. There are 8 remaining objects of lengths c, d, e, . . . j. Call the average of these lengths x, which is what we want to find. sum of lengths of remaining objects (a b are not present because only cd...j remain)

cde...j Average length x 8 number of remaining objects

Multiply Equation 1 by 10 to get rid of the denominator. We get:

Use equations 1 and 2 :

25 10 250 a b c . . . j Now multiply Equation 2 by 2 to get rid of the denominator: 20 2 40 a b Subtract these two new equations: 250 a b c . . . j [40 a b] You get: 210 cd...j Now you just have to divide by 8 to get:

abc...j 25 10

1

ab 20 2

2

210 cd...j x 8 8 1 26 4

MATH GY STRATE

Know How to Manipulate Inequalities Most problems involving inequalities can be solved by remembering one of the following statements. If x 0 and z x y, then z y

If x y, then x z y z

Statement 1

If x y and w z, then x w yz

Statement 2

If w 0 and x y, then wx wy

Statement 3

If w 0 and x y, then wx wy

Statement 4

If x y and y z, then x z

Statement 5

x y is the same as y x

Statement 6

If xy 0, then x 0 and y 0 or x 0 and y 0

Statement 12

a x b is the same as both a x and x b

Statement 7

If xy 0, then x 0 and y 0 or x 0 and y 0

Statement 13

If x y 0 and w z 0, then xw yz

Statement 9

Note that Statement 1 and Statement 2 are also true if all the “” signs are changed to “ ” signs

Statement 8

If x 0, then

xn 0 if n is odd

Statement 10

xn 0 if n is even

Statement 11

6

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EXAMPLE 1

See Statement 3 : Multiply 1 by b. We get

a b b(1) b

If 0 x 1, then which of the following must be true? I. 2x 2 II. x 1 0 III. x2 x (A) (B) (C) (D) (E)

a b

4

1 Use Statement 3 where w : Divide 4 by a. a We get

I only II only I and II only II and III only I, II, and III

a b a a b 1 a

Choice E is correct. We are told that 0 x 1. Using Statement 7 , we have 0 x x 1

or b 1 a

1 2

For Item I, we multiply 2 by 2.

EXAMPLE 3

See Statement 3 2x 2 Thus, Item I is true. For Item II, we add 1 to both sides of 2 .

Which combination of the following statements can be used to demonstrate that x is positive? I. x y II. 1 y

See Statement 1 to get x1 0

(A) (B) (C) (D) (E)

Thus Item II is true. For Item III, we multiply 2 by x. See Statement 3 to get x2 x

I alone but not II II alone but not I I and II taken together but neither taken alone Both I alone and II alone Neither I nor II nor both

Choice C is correct. We want to know which of the following

Thus, Item III is true. All items are true, so Choice E is correct.

xy 1 y

EXAMPLE 2

1 2

is enough information to conclude that a Given that is less than 1, a 0, b 0. Which of the b following must be greater than 1? a (A) 2b b (B) 2a b (C) a b (D) a a 2 (E) b


x0

1 alone is not enough to determine 3 because 0 x y could be true. (Note: x is greater than y, but they both could be negative.) 2 alone is not enough to determine 3 because we don’t know whether x is greater than, less than, or equal to y. However, if we use 1 and 2 together, we can compare the two: 1 y is the same as y 1 Therefore, x y with y 1 yields: Statement 5 x1

a Given: 1 b a0 b0

1 2 3

3

Since 1 0 is always true, then from 4 x 0 is always true

4

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Thus, q 0 From 8 , we can say q5 0 or q5 0

EXAMPLE 4

What are all values of x such that (x 7)(x 3) is positive? (A) x 7 (B) 7 x 3 (C) 3 x 7 (D) x 7 or x 3 (E) x 3 or x 7

8 9

Using Statement 5 , combining 4 and 9 , 10 p3 q 5 0 and p3 0. Thus p 0 Using 8 and 10 , it is easily seen that Choice B is correct. Method 2: (Use Strategy 6: Know how to interpret inequalities.) Given: p2 q3 0 p3 q5 0

Choice D is correct. (x 7)(x 3) 0 when x 7 0 and x 3 0 or x 7 0 and x 3 0

1 2

Since p2 is always 0, using this with 1 , we know that q3 0 and, therefore, q 0 3 If q3 0 then q5 0.

Statement 12 From 1 we have x 7 and x 3

3

when x 7 then 3 and 1 are always satisfied.

4

From 2 , we have x 7 and x 3

5

when x 3 then 5 and 2 are always satisfied.

6

1 2

4

Using 4 and 2 we know that p3 0, and therefore p 0 5 Using 3 and 5 , only Choice B is correct.

Thus, 4 and 6 together represent the entire solution. EXAMPLE 5

EXAMPLE 6

If p and q are nonzero real numbers and if p2 q3 0 and if p3 q5 0, which of the following number lines shows the relative positions of p, q, and 0?

Janie is older than Tammy, but she is younger than Lori. Let j, t, and l be the ages in years of Janie, Tammy, and Lori, respectively. Which of the following is true? (A) (B) (C) (D) (E)

j t l t j l t l j l j t l t j

Choice B is correct. (First, use Strategy 2: Translate from words to algebra.) Janie is older than Tammy but she is younger than Lori, translates to:

Choice B is correct. Method 1: Given: p2 q3 0 p3 q5 0

1 2

Subtracting p2 from 1 and q5 from 2 , we have q3 p2 p3 q5

3 4

But p2 0 so p2 0 5 Using Statement 5 , combining 3 and 5 we get q3 p2 0 6 and get q3 0 7

Janie’s age Tammy’s age Janie’s age Lorie’s age

1 2

Given: Janie’s age j Tammy’s age t Lori’s age l

3 4 5

Substituting 3 , 4 , and 5 into 1 and 2 , we get jt j l

6 7

Use Statement 5 . Reversing 6 , we get t j Combining 8 and 7 , we get t j l

8

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MATH GY STRATE

Use Specific Numerical Examples to Prove or Disprove Your Guess When you do not want to do a lot of algebra, or when you are unable to prove what you think is the answer, you may want to substitute numbers.

EXAMPLE 1

The sum of the cubes of any two consecutive positive integers is always (A) (B) (C) (D) (E)

an odd integer an even integer the cube of an integer the square of an integer the product of an integer and 3

Choice A is correct. Try specific numbers. Call consecutive positive integers 1 and 2. Sum of cubes: 13 23 1 8 9 You have now eliminated choices B and C. You are left with choices A, D, and E. Now try two other consecutive integers: 2 and 3 23 33 8 27 35 Choice A is acceptable. Choice D is false. Choice E is false.

Now look for the choice that gives you 8 with m 10. (A) m 10 10 10 20 (B) m 10 10 10 0 (C) m 2 10 2 8—that’s the one EXAMPLE 3

(3x)3 If x 0, then 3x3 (A) (B) (C) (D) (E)

9 1 1 3 9

Choice E is correct. Try a specific number. Let x 1. Then: (3x)3 (3(1))3 (3)3 9 3 3 3x 3(1 ) 33

Thus, Choice A is the only choice remaining. EXAMPLE 4 EXAMPLE 2

John is now m years old and Sally is 4 years older than John. Which represents Sally’s age 6 years ago? (A) (B) (C) (D) (E)

m 10 m 10 m2 m4 4m 6

Choice C is correct. Try a specific number. Let m 10 John is 10 years old. Sally is 4 years older than John, so Sally is 14 years old. Sally’s age 6 years ago was 8 years.

If a 4b, then the average of a and b is 1 (A) b 2 3 (B) b 2 5 (C) b 2 7 (D) b 2 9 (E) b 2 Choice C is correct.

7

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Try a specific number. Let b 1. Then a 4b 4. So the average

EXAMPLE 7

l4 5 . 2 2 5 Look at choices where b 1. The only choice that gives 2 is Choice C. In the figure of intersecting lines above, which of the following is equal to 180 a?

EXAMPLE 5

The sum of three consecutive even integers is P. Find the sum of the next three consecutive odd integers that follow the greatest of the three even integers. (A) (B) (C) (D) (E)

P9 P 15 P 12 P 20 None of these.

(A) (B) (C) (D) (E)

ad a 2d cb b 2a cd

Choice A is correct. Try a specific number. Let a 20°


So, 2 4 6 P 12.

Then 2a 40° Be careful now—all of the other angles are now determined, so don’t choose any more. Because vertical angles are equal, 2a b, so

The next three consecutive odd integers that follow 6 are:

b 40° .

Try specific numbers. Let the three consecutive even integers be 2, 4, 6.

7, 9, 11

Now c b 180°, so c 40 180 and

So the sum of 7 9 11 27. Now, where P 12, look for a choice that gives you 27: (A) P 9 12 9 21—NO (B) P 15 12 15 27—YES

If 3 a, which of the following is not true? 33a3 33a3 3(3) a(3) 333a 3 a (E) 3 3

(A) (B) (C) (D)

Choice D is correct. Try specific numbers. Work backward from Choice E if you wish. Let a 1. Choice E: TRUE STATEMENT

Choice D: 3 3 3 a 3 l or 0 2

Thus, d 140° (vertical angles are equal). Now look at the question: 180 a 180 20 160 Which is the correct choice? (A) a d 20 140 160—that’s the one!

EXAMPLE 6

3 a 1 3 3 3

c 140° .

FALSE STATEMENT

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MATH GY T S RATE

When Each Choice Must Be Tested, Start with Choice E and Work Backward If you must check each choice for the correct answer, start with Choice E and work backward. The reason for this is that the test maker of a question in which each choice must be tested often puts the correct answer as Choice D or E. In this way, the careless student must check all or most of the choices before finding the correct one. So if you’re trying all the choices, start with the last choice, then the next to last choice, etc.

EXAMPLE 1

If p is a positive integer, which could be an odd integer? (A) (B) (C) (D) (E)

2p 2 p3 p p2 p p2 p 7p 3

If you had started with Choice A, you would have had to test four choices, instead of one choice before finding the correct answer. EXAMPLE 3

Choice E is correct. Start with Choice E first since you have to test out the choices. Method 1: Try a number for p. Let p 1. Then (starting with choice E) 7p 3 7(1) 3 4. 4 is even, so try another number for p to see whether 7p 3 is odd. Let p 2. 7p 3 7(2) 3 11. 11 is odd. Therefore, Choice E is correct. Method 2: Look at Choice E. 7p could be even or odd, depending on what p is. If p is even, 7p is even. If p is odd, 7p is odd. Accordingly, 7p 3 is either even or odd. Thus, Choice E is correct. Note: By using either Method 1 or Method 2, it is not necessary to test the other choices.

1 Which fraction is greater than ? 2 4 (A) 9 17 (B) 35 6 (C) 13 12 (D) 25 8 (E) 15 Choice E is correct. Look at Choice E first. l 8 Is ? 2 15 Use the cross-multiplication method.

EXAMPLE 2

If y x2 3, then for which value of x is y divisible by 7? (A) (B) (C) (D) (E)

1 8 So, 2 15

10 8 7 6 5

Choice E is correct. Since you must check all of the choices, start with Choice E: y 52 3 25 3 28 28 is divisible by 4 (Answer)

1 2

8 15

15

16

15

16

8 1 You also could have looked at Choice E and said 16 2 8 1 8 and realized that because has a smaller 15 2 15 8 denominator than . 16

8

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EXAMPLE 4

If n is an even integer, which of the following is an odd integer? (A) (B) (C) (D) (E)

n2 2 n4 (n 4)2 n3 n2 n 1

Choice E is correct. Look at Choice E first. n2 n 1 If n is even n2 is even n is even 1 is odd So, n n 1 even even odd odd. 2

EXAMPLE 5

EXAMPLE 7

Which choice describes a pair of numbers that are unequal? 1 11 (A) , 6 66 34 (B) 3.4, 10 15 1 (C) , 75 5 3 (D) , 0.375 8 86 42 (E) , 24 10 Choice E is correct. Look at Choice E first. 86 24 Cross multiply: 86 24

Which of the following is an odd number? (A) (B) (C) (D) (E)

7 22 59 15 55 35 75 15 47

42 10 42 10 24 42 ends in 8

860 ends in 0

Thus, the numbers must be different and unequal. EXAMPLE 8

Choice D is correct. Look at Choice E first. 47 is even, since 4 4 4 . . . is even 75 So now look at Choice D: 5, which is odd. 5

3 2 8 28

3

4

1

6

3 203

EXAMPLE 6

In the above addition problem, the symbol describes a particular digit in each number. What must be in order to make the answer correct?

6

If and are different digits in the correctly calculated multiplication problem above, then could be (A) (B) (C) (D) (E)

?

1 2 3 4 6

(A) (B) (C) (D) (E)

7 6 5 4 3


Choice E is correct. Try Choice E first. 3 2 8 28

9

3 6 2 8 28 9 9

9 and 6 are different numbers, so Choice E is correct.

Try substituting the number in Choice E first for the . 3 33 4 43 1 31 6 63 3 33 203 0 23 Since you get 203 for the addition, Choice E is correct.

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MATH GY T S RATE

9

Know How to Solve Problems Using the Formula R T D Almost every problem involving motion can be solved using the formula RTD or rate elapsed time distance

EXAMPLE 1

EXAMPLE 2

The diagram below shows two paths: Path 1 is 10 miles long, and Path 2 is 12 miles long. If Person X runs along Path 1 at 5 miles per hour and Person Y runs along Path 2 at y miles per hour, and if it takes exactly the same amount of time for both runners to run their whole path, then what is the value of y?

(A) 2


(B) 41/6

Use R T D. Call distance both cars travel, D (since distance is same for both cars).

(C) 6 (D) 20 (E) 24

So we get:

Choice C is correct. Let T Time (in hours) for either runner to run the whole path. Using R T D, for Person X, we have (5 mi/hr)(T hours) 10 miles or 5T 10 or T2 For Person Y, we have ( y mi/hr)(T hours) 12 miles or yT 12 Using 1 y(2) 12 or y 6

A car traveling at 50 miles per hour for two hours travels the same distance as a car traveling at 20 miles per hour for x hours. What is x? 4 (A) 5 5 (B) 4 (C) 5 (D) 2 1 (E) 2

50 2 D(100) 20 x D(100)

1 2

Solving 2 you can see that x 5. EXAMPLE 3

1 John walks at a rate of 4 miles per hour. Sally walks at a rate of 5 miles per hour. If both John and Sally both start at the same starting point, how many miles is one person from the other after T hours of walking? (Note: Both are walking on the same road in the same direction.) t (A) 2 (B) t (C) 2t 4 (D) t 5 5 (E) t 4 Choice B is correct.

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Draw a diagram:

Dividing Equation 2 by 20 we get:

John (4 mph)

D T2 20 Now add T1 T2 and we get:

Sally (5 mph)

D D T1 T2 1 10 20 Factor D:

Let DJ be distance that John walks in t hours. Let DS be distance that Sally walks in t hours. Then, using R T D,

1 1 1 D 10 20

for John: 4 t DJ for Sally: 5 t DS The distance between Sally and John after T hours of walking is: DS DJ 5t 4t t

1 1 Add . Remember the fast way of adding 10 20 fractions? 1 10

EXAMPLE 4

A man rode a bicycle a straight distance at a speed of 10 miles per hour and came back the same distance at a speed of 20 miles per hour. What was the man’s total number of miles for the trip back and forth, if his total traveling time was 1 hour?

1 30 20 10 20 200 20 10

So: 30 1 (D) 200 Multiply by 200 and divide by 30 and we get:

(A) 15 (B) 7 1/2

200 2 D; D 6 30 3

(C) 6 1/3

1 Don’t forget, we’re looking for 2D: 2D 13 3

(D) 6 2/3 (E) 13 1/3

EXAMPLE 5

Choice E is correct. Always use R T D (Rate Time Distance) in problems like this. Call the first distance D and the time for the first part, T1. Since he rode at 10 mph: 10 T1 D

1

Now for the trip back. He rode at 20 mph. Call the time it took to go back, T2. Since he came back the same distance, we can call that distance D also. So for the trip back using R T D, we get: 20 T2 D

2

Since it was given that the total traveling time was 1 hour, the total traveling time is: T1 T2 1 Now here’s the trick: Let’s make use of the fact that T1 T2 1. Dividing Equation 1 by 10 we get: D T1 10

What is the average rate of a bicycle traveling at 10 mph a distance of 5 miles and at 20 mph the same distance? (A) 15 mph (B) 20 mph (C) 12 1/2 mph (D) 13 1/3 mph (E) 16 mph Choice D is correct. Ask yourself, what does average rate mean? It does not mean the average of the rates! If you thought it did, you would have selected Choice A as the answer (averaging 10 and 20 to get 15)—the “lure” choice. Average is a word that modifies the word rate in this case. So you must define the word rate first, before you do anything with averaging. Since Rate Time Distance, D istance Rate T ime

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Then average rate must be: TOTAL distance Average rate TOTAL time The total distance is the distance covered on the whole trip, which is 5 5 10 miles. The total time is the time traveled the first 5 miles at 10 mph added to the time the bicycle traveled the next 5 miles at 20 mph. Let t1 be the time the bicycle traveled first 5 miles. Let t2 be the time the bicycle traveled next 5 miles. Then the total time t1 t2. Since R T D, for the first 5 miles: 10 t1 5 for the next 5 miles: 20 t2 5 5 Finding t1: t1 10 5 Finding t2: t2 20 5 5 So, t1 t2 10 20 1 1 2 4 42 (remembering how to quickly add 8 fractions) 6 3 8 4

TOTAL DISTANCE Average rate TOTAL TIME 55 3 4 4 (5 5) 3 4 40 1 10 13 (Answer) 3 3 3 Here’s a formula you can memorize: If a vehicle travels a certain distance at a mph and travels the same distance at b mph, the average rate is 2ab . ab Try doing the problem using this formula: 2 (10) (20) 400 1 2ab 13 10 20 30 3 ab Caution: Use this formula only when you are looking for average rate and when the distance is the same for both speeds.

MATH GY STRATE

10

Know How to Use Units of Time, Distance, Area, or Volume to Find or Check Your Answer By knowing what the units in your answer must be, you will often have an easier time finding or checking your answer. A very helpful thing to do is to treat the units of time or space as variables (like “x” or “y”). Thus, you should substitute, multiply, or divide these units as if they were ordinary variables. The following examples illustrate this idea. EXAMPLE 1

What is the distance in miles covered by a car that traveled at 50 miles per hour for 5 hours? (A) (B) (C) (D) (E)

10 45 55 200 250

Choice E is correct. Although this is an easy “R T D” problem, it illustrates this strategy very well. Recall that rate time distance (50 mi./hr.)(5 hours) distance Notice that when I substituted into R T D, I kept the units of rate and time (miles/hour and hours). Now I will treat these units as if they were ordinary variables. Thus, distance (50 mi./hr.)(5 hours)

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I have canceled the variable “hour(s)” from the numerator and denominator of the right side of the equation. Hence, distance 250 miles The distance has units of “miles” as I would expect. In fact, if the units in my answer had been “miles/hour” or “hours,” then I would have been in error. Thus, the general procedure or problems using this strategy is: Step 1. Keep the units given in the question. Step 2. Treat the units as ordinary variables. Step 3. Make sure the answer has units that you would expect.

EXAMPLE 3

A car wash cleans x cars per hour, for y hours at z dollars per car. How much money in cents did the car wash receive? xy (A) 100z xyz (B) 100 (C) 100xyz 100x (D) yz yz (E) 100x Choice C is correct.

EXAMPLE 2

How many inches is equivalent to 2 yards, 2 feet, and 7 inches? (A) (B) (C) (D) (E)

x cars z dollars ) xyz dollars Use units: ( y hours hour car 1

Multiply 1 by 100. We get 100xyz cents.

11 37 55 81 103

EXAMPLE 4

Choice E is correct. Remember that 1 2

1 yard 3 feet 1 foot 12 inches

Treat the units of length as variables! Divide 1 by 1 yard, and 2 by 1 foot, to get 3 feet 1 1 yard

3

12 inches 1 1 foot

4

We can multiply any expression by 1 and get the same value. Thus, 2 yards 2 feet 7 inches (2 yards)(1)(1) (2 feet)(1) 7 inches

3 feet 12 inches 12 inches 2 yards 2 feet 7 yard f oot f oot inches

Choice B is correct. Know how to work with units. Given: 3 feet 1 yard 12 inches 1 foot

5

Substituting 3 and 4 into 5 , 2 yards 2 feet 7 inches

There are 3 feet in a yard and 12 inches in a foot. How many yards are there altogether in 1 yard, 1 foot, and 1 inch? 1 (A) 1 3 13 (B) 1 36 11 (C) 1 18 5 (D) 2 12 1 (E) 4 12

72 inches 24 inches 7 inches 103 inches Notice that the answer is in “inches” as I expected. If the answer had come out in “yards” or “feet,” then I would have been in error.

Thus, 1 yard 1 foot 1 inch

1 yard 1 foot 1 inch 12 inches 3 feet 1 yard 1 yard 1 foot 3 feet

1 1 1 yards 3 36 12 1 1 yards 36 36 13 1 yards 36

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MATH GY STRATE

11

Use New Definitions and Functions Carefully Some SAT questions use new symbols, functions, or definitions that were created in the question. At first glance, these questions may seem difficult because you are not familiar with the new symbol, function, or definition. However, most of these questions can be solved through simple substitution or application of a simple definition. EXAMPLE 1

If the symbol is defined by the equation a b a b ab

1 for all a and b, then (3) 3 5 (A) 3 11 (B) 3 13 (C) 3 (D) 4 (E) 5 Choice A is correct. All that is required is substitution:

EXAMPLE 2

5 (x 1) Let x 2 5 x 2

5 (A) y 2

(B) 5y

5 (D) 5y 2

(E) 5y 5

Choice B is correct. All we have to do is to substitute 2y into the definition of x . In order to know which definition of x to use, we want to know if 2y is even. Since y is an integer, then 2y is an even integer. Thus,

1

or

1 Substitute for a and 3 3 for b in a b ab: 1 1 (3) (3) 3 3

1 3 1 3 1 2 3 5 (Answer) 3

5 (C) y 1 2

2y 5 (2y) 2

3 (3)

if x is an even integer

Find 2y , where y is an integer.

a b a b ab

1 (3) 3

if x is an odd integer

2y 5y (Answer)

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EXAMPLE 3

EXAMPLE 5

As in the previous Example 1, ø is defined as a ø b a b ab. If, a ø 3 6, a

is defined as xz yt

9 (A) 2 9 (B) 4

9 (C) 4 4 (D) 9 9 (E) 2 Choice E is correct. a ø b a b ab aø36 Substitute a for a, 3 for b: a ø 3 a 3 a(3) 6 a 3 3a 6 2a 3 6 2a 9 9 a 2


EXAMPLE 4

The symbol

is defined as the greatest integer

xz yt;

?

Substituting 2 for x, 1 for z, 1 for y, and 1 for t,

less than or equal to x. (2)(1) (1)(1) 1 (A) (B) (C) (D) (E)

16 16.6 17 17.6 18

Now work from Choice E:

(E)

EXAMPLE 6

Choice C is correct. is defined as the greatest integer less than or equal to 3.4. This is 4, since 4 3.4. is defined as the greatest integer less than or equal to 21. That is just 21, since 21 21. Thus, 4 21 17

xz yt (3)(1) (1)(2) 321

If for all numbers a, b, c the operation is defined as a b ab a then a (b c) (A) a(bc b 1) (B) a(bc b 1) (C) a(bc c b 1) (D) a(bc b 1) (E) a(b a c) Choice A is correct.

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a b ab a a (b c) ? Find (b c) first. Use substitution: a b ab a ↑ ↑ b c

Now, a (b c) a (bc b) Use definition a b ab a Substitute a for a and bc b for b: a b ab a a (bc b) a (bc b) a abc ab a a(bc b 1)

Substitute b for a and c for b: b c b(c) b

MATH GY STRATE

Try Not to Make Tedious Calculations Since There Is Usually an Easier Way In many of the examples given in these strategies, it has been explicitly stated that one should not calculate complicated quantities. In some of the examples, we have demonstrated a fast and a slow way of solving the same problem. On the actual exam, if you find that your solution to a problem involves a tedious and complicated method, then you are probably doing the problem in a long, hard way.* Almost always there will be an easier way. Examples 3, 7, and 8 can also be solved with the aid of a calculator and some with the aid of a calculator allowing for exponential calculations. However, to illustrate the effectiveness of Math Strategy 12, we did not use the calculator method of solving these examples. EXAMPLE 1

3 If y 4 and y , x 8

Just divide the two equations: (Step 1) y8 4

7

what is the value of y in terms of x? 4x (A) 3 3x (B) 4

3 (Step 2) y7 x

12 (E) x Choice A is correct. 1 Don’t solve for the value of y first, by finding y 4 8

*Many times, you can DIVIDE, MULTIPLY, ADD, SUBTRACT, or FACTOR to simplify.

4x (Step 5) y (Answer) 3

y8 4 (Step 3) 7 y 3 x

4 (C) x x (D) 4

x (Step 4) y 4 3

EXAMPLE 2

If x 1 2 22 23 24 25 26 27 28 29 and y 1 2x, then y x (A) (B) (C) (D) (E)

27 28 29 210 211

Choice D is correct. I hope you did not calculate 1 2 . . . 29. If you did, then you found that x 1,023 and y 2,047 and y x 1,024.

12

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Here is the FAST method. Instead of making these tedious calculations, observe that since x 1 2 22 23 24 25 26 27 28 29

If (a2 a)3 (a 1)3x, where a 1 0, then x 1

then 2x 2 22 23 24 25 26 27 28 29 210

2

and y 1 2x 1 2 2 2 2 25 26 27 28 29 210

3

2

3

EXAMPLE 5

4

Thus, calculating 3 1 , we get y x 1 2 22 23 24 25 26 27 28 29 210 (1 2 22 23 24 25 26 27 28 29) 210 (Answer) EXAMPLE 3

(A) a (B) a2 (C) a3 a1 (D) a a (E) a1 Choice C is correct. Isolate x first: (a2 a)3 x (a 1)3 x3 x 3 Now use the fact that 3 : y y

(a a)3 a2 a 3 (a 1) a1 2

Use factoring to make problems simpler.

(88) (88) (3) 2

2

Now factor a2 a a(a 1) So: a2 a a 1

(A) 88 (B) 176 (C) 348 (D) 350 (E) 352 Choice B is correct. Factor:

a(a 1) a 1

(88)2 (88)2 (3) 882(4) So:

(A) (B) (C) (D) (E)

1 8 1 4 1 2 2 4

3

EXAMPLE 6

p1 If 1 and p, r are nonzero, and p is not equal to r1 1, and r is not equal to 1, then (A) (B) (C) (D) (E)

2 p/r l always p/r 1 always p/r 1 always p/r can be greater than 2 p/r 2 always


Choice B is correct. Divide by 8:

3

a3

882 4 88 2 176

If 16r 24q 2, then 2r 3q

a(a 1)

3

a1

(88)2 (88)2(3) 882(1 3) 882(4)

EXAMPLE 4

3

16r 24q 2 8 8 1 2r 3q 4

Get rid of the fraction. Multiply both sides of the equation p1 1 by r 1! r1 p1 r 1 r 1 r 1

p1r1 Cancel the 1’s: pr So:

p 1 r

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EXAMPLE 7

EXAMPLE 8

4 250

(3 414) 413

(A) (B) (C) (D) (E)

(A) (B) (C) (D) (E)

0.16 0.016 0.0016 0.00125 0.000125

4 12 2 413 3 413 11 413



Don’ t divide 4 into 250! Multiply: 4 4 16 4 250 1,000

Factor 413 from (3 414) 413 We get 413[(3 41) 1] or 413[12 1] 413[11]

16 16 Now .016. 10 0 .16, so 1,000

You will see more of the technique of dividing, multiplying, adding, and subtracting in the next strategy, MATH STRATEGY 13.

MATH GY STRATE

Know How to Find Unknown Expressions by Adding, Subtracting, Multiplying, or Dividing Equations or Expressions When you want to calculate composite quantities like x 3y or m n, often you can do it by adding, subtracting, multiplying, or dividing the right equations or expressions. EXAMPLE 1

EXAMPLE 2

If 4x 5y 10 and x 3y 8, 5x 8y then 3

If 25x 8y 149 and 16x 3y 89, then

(A) (B) (C) (D) (E)

(A) (B) (C) (D) (E)

9x 5y 5

18 15 12 9 6

Choice E is correct. Don’t solve for x, then for y. 5x 8y Try to get the quantity by adding or subtracting 3 the equations. In this case, add equations. 4x 5y 10 x 3y 8 5x 8y 18 Now divide by 3: 5x 8y 18 6 3 3

(Answer)

12 15 30 45 60

Choice A is correct. We are told 25x 8y 149 16x 3y 89

1 2

The long way to do this problem is to solve 1 and 2 9x 5y for x and y, and then substitute these values into 5 The fast way to do this problem is to subtract 2 from 1 and get 9x 5y 60 3 Now all we have to do is to divide 3 by 5 9x 5y 12 5

(Answer)

13

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EXAMPLE 6

EXAMPLE 3

x3 If x 0, y 0 and x2 27 and y 2 3, then 3 y

If 21x 39y 18, then 7x 13y (A) (B) (C) (D) (E)


Choice B is correct. We are given 21x 39y 18 Divide 1 by 3: 7x 13y 6

(Answer)

EXAMPLE 4

If x 2y 4, then 5x 10y 8 (A) (B) (C) (D) (E)

9 27 36 48 54

Choice B is correct. x2 27 Divide: 2 9 3 y x Take square root: 3 y 3

x3

y 3 27

x So y

3

3

EXAMPLE 7

10 12 10 12 0

m 3 m 4 n If and , then n q q 7 8

Choice B is correct. Multiply x 2y 4 by 5 to get: 5x 10y 20 Now subtract 8: 5x 10y 8 20 8 12 EXAMPLE 5

1 If 6x y and x , then y y 5

1

(A) (B) (C) (D) (E)

2

(A) x6 x5 (B) 6

12 (A) 1 5 12 (B) 56 56 (C) 12 32 (D) 21 21 (E) 3 2 Choice D is correct. First get rid of fractions! m 3 Cross-multiply to get 8m ⴝ 3n. n 8 m 4 Now cross-multiply to get 7m ⴝ 4q. q 7

1 2

Now divide equations 1 and 2 :

(C) 6x6

8m 3n 7m 4q

6x5 (D) 5

3

The m’s cancel and we get:

x5 (E) 5 Choice C is correct. 1 Multiply 6x5 y 2 by x y to get: 1 6x 6 y 2 y y

8 3n 7 4q

4

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Multiply Equation 4 by 4 and divide by 3 to get

We have a b cd 20 4 b c d 10 3

84 n . 73 q n 32 . q 21

Thus

1 2

Multiply Equation 1 by 4: EXAMPLE 8

a b c d 80

3

Now multiply equation 2 by 3:

abcd If 20 4 bcd And 10 3 Then a (A) (B) (C) (D) (E)

We get: We get:

b c d 30

4

Now subtract Equation 4 from Equation 3 :

We get a 50.

50 60 70 80 90

3 4

a b c d 80 (b c d 30)

MATH GY STRATE

Choice A is correct.

14

Draw or Extend Lines in a Diagram to Make a Problem Easier; Label Unknown Quantities EXAMPLE 1

The circle with center A and radius AB is inscribed in the square to the left. AB is extended to C. What is the ratio of AB to AC ? (A) 2

2 (B) 4 2 1 (C) 2 2 (D) 2 (E) None of these. Choice D is correct. Always draw or extend lines to get more information. Also label unknown lengths, angles, or arcs with letters.

Label AB a and BC b. Draw perpendicular AD. Note it is just the radius, a. CD also a, because each side of the square is length 2a (the 1 diameter) and CD is the side of the square. 2 a AB We want to find ab AC Now ADC is an isosceles right triangle so AD CD a. By the Pythagorean Theorem, a2 a2 (a b)2 where a b is hypotenuse of right triangle. We get: 2a2 (a b)2 Divide by (a b)2: 2a 2 2 1 (a b)

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Divide by 2:

EXAMPLE 3 2

a 1 2 (a b) 2 Take square roots of both sides: a 1 (a b) 2 1 2 2 2

2 2

(Answer)

EXAMPLE 2

In the figure above, O is the center of a circle with a radius of 6, and AOCB is a square. If point B is on the circumference of the circle, the length of AC (A) (B) (C) (D) (E)

6 2 3 2 3 6 6 3


What is the perimeter of the above figure if B and C are right angles? (A) (B) (C) (D) (E)


This is tricky if not impossible if you don’t draw OB. So draw OB:


Draw perpendicular AE. Label side BC h. You can see that AE h.

Since AOCB is a square, OB AC; and since OB radius 6, AC 6.

ABCE is a rectangle, so CE 3. This makes ED 3 since the whole DC 6.

EXAMPLE 4

Now use the Pythagorean Theorem for triangle AED: h2 32 52 h2 52 32 h2 25 9 h2 16 h4 So the perimeter is 3 h 6 5 3 4 6 5 18 (Answer)

1 Lines ᐉ1 and ᐉ2 are parallel. AB 3AC. The area of triangle ABD The area of triangle DBC

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104 • STRATEGY SECTION EXAMPLE 5

1 (A) 4 1 (B) 3 3 (C) 8 1 (D) 2 (E) Cannot be determined. Choice D is correct. 1 AB AC 3

(Note: Figure is not drawn to scale.) The area of the above figure ABCD

Ask yourself, what is the area of a triangle? It is 1⁄2 (height base). So let’s get the heights and the bases of t h e triangles ABD and DBC. First draw the altitude (call it h).

1 Now label AB AC (given) 3 2 This makes BC AC, since AB BC AC 3

1 1 1 Thus the area of ⌬ABD h (AB) h AC 2 2 3 1 1 2 Area of ⌬DBC h (BC) h AC 2 2 3

(A) (B) (C) (D) (E)

is 36 is 108 is 156 is 1,872 Cannot be determined.


Draw BD. BCD is a 3-4-5 right triangle, so BD 5. Now remember that a 5-12-13 triangle is also a right triangle, so angle ABD is a right angle. The area of triangle BCD is (3 4)/2 6 and the area of triangle BAD is (5 12)/2 30, so the total area is 36. EXAMPLE 6

1 1 h AC Area of ABD 2 3 Area of DBC 1 2 h AC 2 3 1 3 1 3 1 2 3 2 2 3

In the above figure, two points, B and C, are placed to the BC right of point A such that 4AB 3AC. The value of AB 1 (A) equals 3 2 (B) equals 3 3 (C) equals 2 (D) equals 3 (E) Cannot be determined. Choice A is correct.

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x is measured by 1⁄2 arc it cuts. 1 So, x (b a 40) 2 1 Likewise, y (c d 40) 2 You want to find x y, so add:

Place B and C to the right of A:

Now label AB a and BC b:

We are given 4AB 3AC So, 4a 3(a b). Expand: 4a 3a 3b Subtract 3a: a 3b

But what is a b c d 40? It is the total number of degrees around the circumference, which is 360. 1 So, x y (( b a c + d 40 40) 2

BC b b is what we want to find a a AB

1 x (b a 40) 2 1 y (c d 40) 2 1 x y (b a 40 c d 40) 2

1 b Divide by 3 and a: 3 a

1 (360 40 ) 2 1 (400) 200 2

1 BC b BC But remember , so 3 AB a AB EXAMPLE 7

In the figure above, ABCDE is a pentagon inscribed in the circle with center at O. DOC 40°. What is the value of x y? (A) 80 (B) 100 (C) 180 (D) 200 (E) Cannot be determined. Choice D is correct.

EXAMPLE 8

In the above figure, if ABE 40°, DBC 60°, and ABC 90°, what is the measure of DBE? (A) (B) (C) (D) (E)

10° 20° 40° 100° Cannot be determined.


Label degrees in each arc. Label angles first. Now ABE 40, so a b 40 DBC 60, so b c 60 ABC 90, so a b c 90

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(B) Relabel, using the fact that vertical angles are equal.

You want to find DBE. DBE b and you want to get the value of b from: 1 a b 40 2 b c 60 3 a b c 90

Now use the fact that a straight angle has 180° in it:

Add 1 and 2 : a b 40 b c 60 a 2b c 100 Subtract 3 (a b c 90) b 10 EXAMPLE 9

Now use the fact that the sum of the angles of a triangle 180°: 180 a 180 b 180 c 180 540 a b c 180 540 180 a b c 360 a b c Now remember what we are looking to find (the sum): a a b b c c 2a 2b 2c In the figure above, three lines intersect at the points shown. What is the value of A B C D E F? (A) (B) (C) (D) (E)

But this is just 2(a b c) 2(360) 720

1,080 720 540 360 Cannot be determined.


MATH GY STRATE

Know How to Eliminate Certain Choices Instead of working out a lot of algebra, you may be able to eliminate several of the choices at first glance. In this way you can save yourself a lot of work. The key is to remember to use pieces of the given information to eliminate several of the choices at once.

EXAMPLE 1

The sum of the digits of a three-digit number is 15. If this number is not divisible by 2 but is divisible by 5, which of the following is the number?

(A) (B) (C) (D) (E)

384 465 635 681 780

15

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Choice B is correct. Use pieces of the given information to eliminate several of the choices. Which numbers are divisible by 2? Choices A and E are divisible by 2 and, thus, can be eliminated. Of Choices B, C, and D, which are not divisible by 5? Choice D can be eliminated. We are left with Choices B and C. Only Choice B (465) has the sum of its digits equal to 15. Thus, 465 is the only number that satisfies all the pieces of the given information. If you learn to use this method well, you can save loads of time. EXAMPLE 2

Which of the following numbers is divisible by 5 and 9, but not by 2? (A) (B) (C) (D) (E)

625 639 650 655 675

Using 1 , we see that Choices B and E each end in 5. All others end in digits less than 5 and may be eliminated. Starting with Choice E (See Strategy 8). 2 Choice E, 2,345, becomes 5,342. 3 Choice B, 4,235, becomes 5,234. 2 is larger than 3 . EXAMPLE 4

Which of the following could be the value of 3x where x is an integer? (A) (B) (C) (D) (E)

339,066 376,853 411,282 422,928 531,441

Choice E is correct. Let’s look at what 3x looks like for integral values of x:

Choice E is correct. Clearly, a number is divisible by 5 if, and only if, its last digit is either 0 or 5. A number is also divisible by 2 if, and only if, its last digit is divisible by 2. Certain choices are easily eliminated. Thus we can eliminate Choices B and C. Method 1: To eliminate some more choices, remember that a number is divisible by 9 if, and only if, the sum of its digits is divisible by 9. Thus, Choice E is the only correct answer. Method 2: If you did not know the test for divisibility by 9, divide the numbers in Choices A, D, and E by 9 to find the answer. EXAMPLE 3

If the last digit and the first digit are interchanged in each of the numbers below, which will result in the number with the largest value? (A) (B) (C) (D) (E)

Certain choices are easily eliminated.

5,243 4,352 4,235 2,534 2,345

Choice E is correct. The numbers with the largest last digit will become the 1 largest numbers after interchanging.

31 3 32 9 33 27 34 81 35 243 36 . . . 9 37 . . . 7 38 . . . 1 Note that 3x always has the units digit ending in 3, 9, 7, or 1. So we can eliminate choices A, C, and D since the units digits in those choices end in other numbers than 3, 9, 7, or 1. We are left with Choices B and E. The number in the correct choice must be exactly divisible by 3 since it is of the form 3x ( 3 3 3 . . .) where x is an integer. This is a good time to use your calculator. Divide the number in choice B by 3: You get 125,617.66. That’s not an integer. So the only remaining choice is Choice E.

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MATH GY STRATE

16

Watch Out for Questions That Seem Very Easy But That Can Be Tricky—Beware of Choice A as a “Lure Choice” When questions appear to be solved very easily, think again! Watch out especially for the “lure” Choice A.

EXAMPLE 1*

6:06

elements. If 0 is included in the list, then there are m 1 elements. Hence, if 0 d m where d is integral, then d can have m 1 different values. EXAMPLE 3

The diagram above shows a 12-hour digital clock whose hour digit is the same as the minutes digit. Consider each time when the same number appears for both the hour and the minutes as a “double time” situation. What is the shortest elapsed time period between the appearance of one double time and an immediately succeeding double time? (A) (B) (C) (D) (E)

61 minutes 60 minutes 58 minutes 50 minutes 49 minutes

There are some flags hanging in a horizontal row. Starting at one end of the row, the U.S. flag is 25th. Starting at the other end of the row, the U.S. flag is 13th. How many flags are in the row? (A) (B) (C) (D) (E)

36 37 38 39 40

Choice B is correct. The obvious may be tricky!

Choice E is correct. Did you think that just by subtracting something like 8:08 from 9:09 you would get the answer (1 hour and 1 minute 61 minutes)? That’s Choice A, which is wrong. So beware, because your answer came too easily for a test like the SAT. You must realize that there is another possibility of double time occurrence— 12:12 and 1:01, whose difference is 49 minutes. This is Choice E, the correct answer.

Method 1: Given: The U.S. flag is 25th from one end. The U.S. flag is 13th from the other end.

At first glance it may appear that adding 1 and 2 , 25 13 38, will be the correct answer. This is WRONG! The U.S. flag is being counted twice: Once as the 25th and again as the 13th from the other end. The correct answer is 25 13 1 37.

EXAMPLE 2

Method 2: The letters d and m are integral digits in a certain number system. If 0 d m, how many different possible values are there for d? (A) (B) (C) (D) (E)

m m1 m2 m1 m2

Choice D is correct. Did you think that the answer was m? Do not be careless! The list 1,2,3, . . . , m contains m *Note: This problem also appears in Strategy 1 of the 5 General Strategies on page 60.

1 2

24 12 U.S. flag 36 U.S. flag 37

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EXAMPLE 4

OR RQ in the figure above. If the coordinates of Q are (5,m), find the value of m. (A) (B) (C) (D) (E)

5 5 0 5 5

Given: OR RQ Coordinates of Q (5,m) From 2 , we get RQ 5 Substitute 3 into 1 . We get OR 5

1 2 3

The obvious may be tricky! Since Q is below the xaxis, its y-coordinate is negative. Thus m 5.


MATH GY T S RATE

17

Use the Given Information Effectively (and Ignore Irrelevant Information) You should always use first the piece of information that tells you the most, or gives you a useful idea, or that brings you closest to the answer. EXAMPLE 1

Use the piece of information that will give you something definite. You might have first thought of using the fact that the sum of the angles of a triangle 180°. However, that will give you a 2y 6y 180 That’s not very useful. However, if you use the fact that the sum of the angles in a straight angle is 180 we get:

(Note: Figure is not drawn to scale.) In the figure above, side BC of triangle ABC is extended to D. What is the value of a? (A) (B) (C) (D) (E)

15 17 20 24 30


6y 3y 180 and we get 9y 180 y 20 Now we have gotten something useful. At this point, we can use the fact that the sum of the angles in a triangle is 180. a 2y 6y 180 Substituting 20 for y, we get a 2(20) 6(20) 180 a 20

(Answer)

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EXAMPLE 2

a The minimum value of is when a is minimum and b b is maximum. The minimum value of a .003 The maximum value of b 300 .003 .001 a So the minimum value of .00001. 300 100 b EXAMPLE 4

If xry 0, yst 0, and rxt 1, then which must be 0? (Note: Figure is not drawn to scale.) Which of the above angles has a degree measure that can be determined? (A) (B) (C) (D) (E)

WOS SOU WOT ROV WOV

(A) (B) (C) (D) (E)

r s t x y

Choice E is correct. Use information that will give you something to work with. rxt 1 tells you that r 0, x 0, and t 0. So if xry 0 then y must be 0.

Choice C is correct. Use information that will get you something useful.

EXAMPLE 5*

4a 2b 360 (sum of all angles 360°) Divide by 2 to simplify: 2a b 180 Now try all the choices. You could work backward from Choice E, but we’ll start with Choice A: (A) WOS 2a—You know that 2a b 180 but don’t know the value of 2a. (B) SOU b a—You know 2a b 180 but don’t know the value of b a. (C) WOT b 2a—You know that 2a b 180, so you know the value of b 2a.

On a street with 25 houses, 10 houses have fewer than 6 rooms, 10 houses have more than 7 rooms, and 4 houses have more than 8 rooms. What is the total number of houses on the street that are either 6-, 7-, or 8-room houses? (A) (B) (C) (D) (E)

5 9 11 14 15



There are three possible situations: EXAMPLE 3

If a ranges in value from 0.003 to 0.3 and b ranges in a value from 3.0 to 300.0, then the minimum value of is b (A) 0.1 (B) 0.01 (C) 0.001 (D) 0.0001 (E) 0.00001 Choice E is correct. Start by using the definition of minimum and maximum.

(a) Houses that have fewer than 6 rooms (call the number a) (b) Houses that have 6, 7, or 8 rooms (call the number b) (c) Houses that have more than 8 rooms (call the number c) a b c must total 25 (given). 1 a is 10 (given). 2 c is 4 (given). 3 Substituting 2 and 3 in 1 we get 10 b 4 25. b must therefore be 11. *This problem also appears in the 14 Questions That Can Determine Top College Eligibility, Part 3.

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EXAMPLE 6

Method 2: Total number of people are:

In a room, there are 5 blue-eyed blondes. If altogether there are 14 blondes and 8 people with blue eyes in the room, how many people are there in the room? (Assume that everyone in the room is blonde, has blue eyes, or is a blue-eyed blonde.) (A) (B) (C) (D) (E)

11 17 22 25 27

Choice B is correct. Method 1: Draw two intersecting circles.

Above, subtracting: all blondes (14) – blue-eyed blondes (5), we get 9. Above, subtracting: all blue-eyed people (8) – blue-eyed blondes (5), we get 3. So the number of people in room are 9 5 3 17.

(a) blondes without blue eyes (b) blue-eyed people who are not blonde (c) blue-eyed blondes (a) There are 14 blondes and 5 blue-eyed blondes, so, subtracting, there are 9 blondes without blue eyes. (b) There are 8 people with blue eyes and 5 blue-eyed blondes, so, subtracting, there are 3 blue-eyed people who are not blonde. (c) The number of blue-eyed blondes is 5 (given). Adding the number of people in a, b, and c, we get 9 ⴙ 3 ⴙ 5 ⴝ 17.

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MATH GY STRATE

18

Know and Use Facts About Triangles By remembering these facts about triangles, you can often save yourself a lot of time and trouble. IV.

I.

Similar Triangles

If a b, then x y

The base angles of an isosceles triangle are equal

If x y, then a b If ABC DEF, then If the base angles of a triangle are equal, the triangle is isosceles

mAmD mBmE mCmF

II.

a b c and d e f V. ᐉ is a straight line. Then, x y z The measure of an exterior angle is equal to the sum of the measures of the remote interior angles III.

m A m B m C 180°

The sum of the interior angles of a triangle is 180 degrees VI.

If a b, then y x AD BC Area of ABC 2 If y x, then a b

In a triangle, the greatest angle lies opposite the greatest side

The area of a triangle is one-half the product of the altitude to a side and the side. Note: If m A 90°, AB AC Area also 2

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VII.

In a right triangle, c2 a2 b2 and x° y° 90°

Method 2: Look at VIII in left column. Notice that MNP is similar to one of the standard triangles:

VIII. Memorize the following standard triangles:

This is true because 12 5 (Look at IV). 24 10 12 13 Hence, or x 26 (Answer) 24 x EXAMPLE 2

If Masonville is 50 kilometers due north of Adamston and Elvira is 120 kilometers due east of Adamston, then the minimum distance between Masonville and Elvira is (A) (B) (C) (D) (E)

125 kilometers 130 kilometers 145 kilometers 160 kilometers 170 kilometers

Choice B is correct. Draw a diagram first. EXAMPLE 1

In the diagram below, what is the value of x?

(A) (B) (C) (D) (E)

20 25 26 45 48

Choice C is correct. Method 1: Use VII above. Then, x2 242 102 576 100 676 Thus, x 5 26 (Answer)

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114 • STRATEGY SECTION EXAMPLE 4

The given information translates into the diagram above. Note Statement VIII on p. 113. The triangle above is a multiple of the special 5, 12, 13 right triangle 50 10(5) 120 10(12) Thus, x 10(13) 130 km (Note: The Pythagorean Theorem could also have been used: 502 1202 x2.) EXAMPLE 3

(Note: Figure is not drawn to scale.) The triangle above has side BC 10, angle B 45°, and angle A 90°. The area of the triangle (A) (B) (C) (D) (E)

is 15 is 20 is 25 is 30 Cannot be determined.

Choice C is correct. First find angle C using V. 90° 45° m C 180° So m C 45°. Using I, we find AB 5 AC, since m B m C 45°. Since our right triangle ABC has BC 10, using 2 2 statement VIII (the right triangle , , 1), multiply 2 2 by 10 to get a right triangle:

(Note: Figure is not drawn to scale.) In triangle ABC, if a c, which of the following is true? (A) (B) (C) (D) (E)

10 2 10 2 , , 10 2 2 10 2 Thus side AB 5 2 2

BC AC AB BC AC AB BC AB BC AC

10 2 side AC 5 2 2

Choice D is correct. (R em em b ertrian g lein eq u alityfacts.) From basic geometry, Statement III, we know that, since m BAC m BCA, then leg opposite BAC leg opposite BCA or BC AB

Now the area of triangle ABC, according to VI is 52 52 25 2 25 2 2

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EXAMPLE 5

Remember triangle facts. Use Statement II. ADB is an exterior angle of ACD, so mADB x x 2x 1 In ADB, the sum of its angles 180 (Statement V), so mADB 55 45 180 or mADB 100 180 or mADB 80 2 Equating 1 and 2 we have

In the figure above what is the value of x? (A) (B) (C) (D) (E)

2x 80 x 40

30 40 50 80 100

(Answer)

MATH GY STRATE


When Calculating Answers, Never Multiply and/or Do Long Division If Reducing Can Be Done First Note: On the SAT exam, because calculators are permitted, you may do the following problems with a calculator also. But it would be wise for you to see the other approach too—how the problem can be solved without the use of a calculator. EXAMPLE 1

Then cancel like factors in numerator and denominator 9 9 15 10 9 5 4 10

81 150 If w , then w 45 40 Reduce further (A) 3 Then simplify

3 (B) 6 4 1 (C) 7 4 (D) 9 1 (E) 20 4

27 3 6 4 4

}

EXAMPLE 2

81 150 and 45 40 to get 12,150 1,800

81 Factor first

(Answer)

Thus, Choice B is correct.

150

Do not multiply in this case.

9 5 3 5 4

45

9 9 15 10 9 5 4 10 40

42 42 42 33 33 33 16 (A) 27 8 (B) 9 4 (C) 3 64 (D) 27 512 (E) 81

19

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Multiply both sides by 27 to get 81 y 21 27

Choice A is correct. 4 4 4 33 33 33 2

2

27 21 y 81

2

3(42) 3(33) 16 27

Factor and reduce:

Factor and reduce:

EXAMPLE 3

y7

12 14 18 If 6 7 8 9 , then x x (A) (B) (C) (D) (E)

3 7 3 9 y 9 9 3 7 3 3 3

EXAMPLE 5

1 2 1 4 8 12

y2 7y 10 Find the value of rounded to the nearest y2 whole number if y 8.000001

1

(A) (B) (C) (D) (E)

2


Choice B is correct. 12 14 18 Given: 6 7 8 9 x 12 14 18 so that x 6789

Do not multiply the numbers out in the numerator and denominator of 2 ! It is too much work! Rewrite 2 . Factor and reduce: x

EXAMPLE 4

81 y If 21, then y 27 1 (A) 21 1 (B) 7 (C) 3 (D) 7 (E) 21 Choice D is correct. 81 y Given: 21 27

y2 7y 10 Given: y2

(Answer)

1

Factor and reduce: Factor the numerator of 1 . We get ( y 5)( y 2) y 5 y2

2 6 2 7 29 12 14 18 6 7 8 9 6789 222 8 1 8 8

2 3 5 6 16

Substitute 8.000001 in 2 . We have 8.000001 5 3.000001 3

2

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16 Verbal (Critical Reading) Strategies Using Critical Thinking Skills in Verbal Questions (Critical Reading Section)

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4 Sentence Completion Strategies

L. COMP SENT. GY E STRAT

For a Sentence with Only One Blank, Fill the Blank with Each Choice to See the Best Fit* Before you decide which is the best choice, fill the blank with each of the five answer choices to see which word will fit best into the sentence as a whole.

EXAMPLE 1

EXAMPLE 3

He believed that while there is serious unemployment in our auto industry, we should not ————— foreign cars.

In large cities, the number of family-owned grocery stores has fallen so sharply that the opportunity to shop in such a place is ————— occasion.

(A) (B) (C) (D) (E)

(A) (B) (C) (D) (E)

discuss regulate research import disallow

a celebrated an old a fanciful a rare an avid

EXPLANATORY ANSWER

EXPLANATORY ANSWER

Choice D is correct. The word “import” means to bring in from another country or place. The sentence now makes good sense. The competition resulting from importation of foreign cars reduces the demand for American-made cars. This throws many American auto workers out of jobs.

Choice D is correct. A rare occasion is one that you seldom have the opportunity to participate in. Shopping in a family-owned grocery store in a large city today is, indeed, a rare occasion.

EXAMPLE 2

Legal ————— initiated by the government necessitate that manufacturers use ————— in choosing food additives.

His attempt to ————— his guilt was betrayed by the tremor of his hand as he picked up the paper. (A) (B) (C) (D) (E)

extenuate determine conceal intensify display

EXAMPLE 4

(A) (B) (C) (D) (E)

entanglements . . knowledge devices . . intensification talents . . decretion proclivities . . moderation restraints . . caution EXPLANATORY ANSWER

EXPLANATORY ANSWER

Choice C is correct. The word “conceal” means to keep secret or to hide. The sentence now makes good sense. The nervousness caused by his guilty conscience is shown by the shaking of his hand. He is thus prevented in his attempt to hide his guilt.

Choice E is correct. Although this is a two-blank question, we should use Sentence Completion Strategy 1. Try the words in each of the choices in the blanks in the sentence. Another possibility is Choice A. But the point of the sentence evidently is that government prohibitions of certain food additives necessitate care by manufacturers in choosing food additives that are permitted. Thus Choice A is not as good as Choice E.

*Strategy 1 is considered the Master Strategy for one-blank Sentence Completion questions because it can be used effectively to answer every one-blank Sentence Completion question. However, it is important that you learn all of the other Sentence Completion Strategies because they can be used to double-check your answers.

1

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EXAMPLE 5

EXAMPLE 6

It is unthinkable for a prestigious conductor to agree to include ————— musicians in his orchestra.

A desire to be applauded by those in attendance, not his sensitivity to the plight of the underprivileged, was the reason for his ————— at the charity affair.

(A) (B) (C) (D) (E)

capable seasoned mediocre recommended professional

(A) (B) (C) (D) (E)

shyness discomfort surprise arrogance generosity

EXPLANATORY ANSWER EXPLANATORY ANSWER

Choice C is correct. The word “mediocre” (meaning average, ordinary) completes the sentence so that it makes good sense. The other choices do not do that.

Choice E is correct. No other choice makes sense in the sentence. It is clear that the person was primarily interested in being appreciated for his donation.


For a Sentence with Two Blanks, Begin by Eliminating the Initial Words That Don’t Make Sense in the Sentence* This strategy consists of 2 steps. Step 1. Find out which “first words” of the choices make sense in the first blank of the sentence. Don’t consider the second word of each pair yet. Eliminate those choices that contain “first words” that don’t make sense in the sentence. Step 2. Now consider the remaining choices by filling in the pair of words for each choice. EXAMPLE 1

STEP 1 [ELIMINATION]

The salesmen in that clothing store are so ————— that it is impossible to even look at a garment without being ————— by their efforts to convince you to purchase.

We have eliminated Choice (C) extensive . . . induced because saying salesmen who are “extensive” does not make sense here. We have eliminated Choice (D) immune . . aided because salesmen who are “immune” does not make sense here.

(A) (B) (C) (D) (E)

offensive . . considerate persistent . . harassed extensive . . induced immune . . aided intriguing . . evaluated EXPLANATORY ANSWER


STEP 2 [REMAINING CHOICES]

This leaves us with these remaining choices to be considered. Choice (A) offensive . . considerate. The sentence does not make sense. Choice (B) persistent . . harassed. The sentence does make sense. Choice (E) intriguing . . evaluated. The sentence does not make sense.

*Strategy 2 is considered the Master Strategy for two-blank Sentence Completion questions because it can be used effectively to answer every two-blank Sentence Completion question. However, it is important to learn all of the other Sentence Completion Strategies because they can be used to doublecheck your answers.

2

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EXAMPLE 2

EXPLANATORY ANSWER

Television in our society is watched so ————— that intellectuals who detest the “tube” are —————–—–.

Choice B is correct. We can first eliminate Choice (A) inconsistently, Choice (C) haphazardly, and Choice (D) secretly because these first blank words do not make sense in the sentence. This leaves us with Choice (B) drastically and Choice (E) doubtlessly. But Choice (E) doubtlessly . . . destroyed does not make sense. Choice (B) drastically . . . abolished does make sense.

(A) (B) (C) (D) (E)

reluctantly . . offended stealthily . . ashamed frequently . . revolted intensely . . exultant noisily . . amazed

EXAMPLE 5

EXPLANATORY ANSWER

Choice C is correct. We have eliminated Choice A because television is not watched reluctantly in our society. We have eliminated Choice B because television is not watched stealthily in our society. We have eliminated Choice E because it is not common for the viewer to watch television noisily. This leaves us with these remaining choices to be considered. Choice D—intensely . . . exultant. The sentence does not make sense. Choice C— frequently . . . revolted. The sentence does make sense.

The report indicates that the crime rate in the United States remains ————— and that one in every three households ————— some form of major crime in any year. (A) (B) (C) (D) (E)

incredible . . visualizes astronomical . . experiences simultaneous . . welcomes unsuccessful . . initiates constant . . anticipates

EXAMPLE 3

EXPLANATORY ANSWER

In view of the company’s ————— claims that its scalp treatment would grow hair on bald heads, the newspaper ————— its advertising.

Choice B is correct. Examine the first word of each choice. We eliminate Choice (C) simultaneous and Choice (D) unsuccessful because it does not make sense to say that the crime rate remains simultaneous or successful. Now we consider Choice (A), which does not make sense in the sentence; Choice B, does make sense; and Choice E does not make sense.

(A) (B) (C) (D) (E)

unproved . . banned interesting . . canceled unreasonable . . welcomed innocent . . settled immune . . questioned

EXAMPLE 6 EXPLANATORY ANSWER

Choice A is correct. The first step is to examine the first words of each choice. We eliminate Choice (D) innocent . . . and Choice (E) immune . . . because “claims” are not innocent or immune. Now we go on to the remaining choices. When you fill in the two blanks of Choice B and of Choice C, the sentence does not make sense. So these two choices are also incorrect. Filling in the two blanks of Choice A makes the sentence meaningful. EXAMPLE 4

The renowned behaviorist B. F. Skinner believed that those colleges set up to train teachers should ———— change their training philosophy, or else be —————————————. (A) (B) (C) (D) (E)

inconsistently . . supervised drastically . . abolished haphazardly . . refined secretly . . dedicated doubtlessly . . destroyed

The discouragement and ———— that so often plague perfectionists can lead to decreases in ————— and production. (A) (B) (C) (D) (E)

pressure . . creativity uplift . . motivation enthusiasm . . efficiency boredom . . idleness involvement . . laziness EXPLANATORY ANSWER

Choice A is correct. Examine the first word of each choice. Choice (B) uplift and Choice (C) enthusiasm do not make sense because “uplift” and “enthusiasm” are not likely to plague any person. Now consider the other choices. Choice (D) boredom . . idleness and Choice (E) involvement . . laziness do not make sense in the sentence as a whole. Choice (A) pressure . . creativity does make sense.

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3

Try to Complete the Sentence in Your Own Words Before Looking at the Choices This strategy often works well, especially with one-blank sentences. You may be able to fill in the blank with a word of your own that makes good sense. Then look at the answer choices to see whether any of the choices has the same meaning as your own word. EXAMPLE 1

Many buildings with historical significance are now being ————— instead of being torn down. (A) (B) (C) (D) (E)

built forgotten destroyed praised repaired EXPLANATORY ANSWER

Choice E is correct. The key words “instead of” constitute an opposite indicator. The words give us a good clue—we should fill the blank with an antonym (opposite) for “torn down.” If you used the strategy of trying to complete the sentence before looking at the five choices, you might have come up with any of the following appropriate words: remodeled reconstructed remade renovated

pacify soothe satisfy conciliate relieve These words all mean the same as the Choice A word, “appease.” EXAMPLE 3

Just as the person who is kind brings happiness to others, so does he bring ————— to himself. (A) (B) (C) (D) (E)

wisdom guidance satisfaction stinginess insecurity EXPLANATORY ANSWER

These words all mean the same as the correct Choice E word, “repaired.” EXAMPLE 2

Wishing to ————— the upset passenger who found a nail in his steak, the flight attendant offered him a complimentary bottle of champagne. (A) (B) (C) (D) (E)

sentence before looking at the five choices, you might have come up with the following words that would have the meaning of “to make someone feel better”:

appease berate disregard reinstate acknowledge EXPLANATORY ANSWER

Choice A is correct. Since the passenger was upset, the flight attendant wished to do something to make him feel better. If you used the strategy of trying to complete the

Choice C is correct. You must look for a word that balances with “happiness.” Here are some of the words: joy goodness satisfaction enjoyment All these words can be linked to Choice C. EXAMPLE 4

Actors are sometimes very ————— since they must believe strongly in their own worth and talents. (A) (B) (C) (D) (E)

laconic unequivocal tedious egotistic reticent

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EXPLANATORY ANSWER

EXPLANATORY ANSWER

Choice D is correct. “Since” signifies result. So the second clause of the sentence, starting with “since,” really tells us that the missing word or words must be

Choice B is correct. You might have come up with any of the following words: susceptible (to) open (to) unprotected (from)

boastful very much interested in one’s own self egotistic self-centered

These words all mean about the same as the correct one, Choice B: “vulnerable.”

Thus, Choice D is correct. EXAMPLE 5

Hunger has reached epidemic proportions nationwide, leaving up to 20 million people ————— to illness and fear. (A) (B) (C) (D) (E)

agreeable vulnerable obvious acclimated sensitive


Pay Close Attention to the Key Words in the Sentence A key word may indicate what is happening in the sentence. Here are some examples of key words and what these words may indicate.

Indicating

Key Word although however in spite of rather than nevertheless on the other hand but

冧

Key Word moreover besides additionally furthermore in fact

Indicating

冧

Key Word therefore consequently accordingly because when so

OPPOSITION

SUPPORT

Indicating

冧

RESULT

4

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There are many other words—in addition to these—that can act as key words to help you considerably in getting the right answer. A key word frequently appears in the sentence. Watch for it! EXAMPLE 1

Richard Wagner was frequently intolerant; moreover, his strange behavior caused most of his acquaintances to ————— the composer whenever possible. (A) (B) (C) (D) (E)


impartial . . worthwhile unique . . reflected spiritual . . inspiring marked . . necessary effective . . interrupted EXPLANATORY ANSWER

EXPLANATORY ANSWER

Choice C is correct. The word “moreover” is a support indicator in this sentence. As we try each choice word in the blank, we find that “shun” (avoid) is the only logical word that fits. You might have selected Choice A (“contradict”), but very few would seek to contradict Wagner because most of his acquaintances tried to avoid him. EXAMPLE 2

Until we are able to improve substantially the ———— status of the underprivileged in our country, a substantial ————— in our crime rate is remote. (A) (B) (C) (D) (E)

(A) (B) (C) (D) (E)

burdensome . . harmony beneficial . . gloom financial . . reduction remarkable . . puzzle questionable . . disappointment EXPLANATORY ANSWER

Choice C is correct. The word “Until” is a result indicator. As we try the first word of each choice in the first blank, we find that “burdensome,” “financial,” and “questionable” all make sense up until the second part of the sentence except “beneficial” and “remarkable.” We therefore eliminate Choices B and D. Now let us try both words in Choices A, C, and E. We then find that we can eliminate Choices A and E as not making sense in the entire sentence. This leaves us with the correct Choice C, which does bring out the result of what is stated in the first part of the sentence. EXAMPLE 3

All of the efforts of the teachers will bring about no ————— changes in the scores of the students because the books and other ————— educational materials are not available.

Choice D is correct. First see Sentence Strategy 2. Let us first eliminate Choices (A) impartial . . . and (C) spiritual . . . because we do not speak of “impartial” or “spiritual” changes. Now note that we have a result situation here as indicated by the presence of the conjunction “because” in the sentence. Choices B and E do not make sense because “unique” changes have nothing to do with “reflected” educational materials, and “effective” changes have nothing to do with “interrupted” educational materials. Choices B and E certainly do not meet the result requirement. Choice D is the only correct choice because it makes sense to say that there will be no “marked” changes in the scores because the books and other “necessary” educational materials are not available. EXAMPLE 4

Being ————— person, he insisted at the conference that when he spoke he was not to be interrupted. (A) (B) (C) (D) (E)

a successful a delightful a headstrong an understanding a solitary EXPLANATORY ANSWER

Choice C is correct. The main clause of the sentence— “he insisted . . . not be interrupted”—supports the idea expressed in the first three words of the sentence. Accordingly, Choice C “headstrong” (meaning stubborn) is the only correct choice. EXAMPLE 5

Although Grete Waitz is a celebrated female marathon runner, she is noted for her ————————————. (A) vigor (B) indecision (C) modesty (D) speed (E) endurance

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EXPLANATORY ANSWER

Choice C is correct. The beginning word “Although” constitutes an opposition indicator. We can then expect the second part of the sentence to indicate an idea that is opposite to what is said in the first part of the sentence. Choice C “modesty” provides the word that gives us the closest to an opposite idea. Since Waitz is celebrated, we expect her to be immodest. The words in the other choices do not give us that opposite idea. For two-blank sentences, look for contrasts or opposition in the two parts of the sentence—then look for opposite relationships in the choices. EXAMPLE 6

EXPLANATORY ANSWER

In spite of the ———— of his presentation, many people were ————— with the speaker’s concepts and ideas.

Choice E is correct. The words in spite of at the beginning of the sentence tell you that the two blanks have an opposite flavor. Watch for opposites in the choices:

(A) (B) (C) (D) (E)

interest . . enthralled power . . taken intensity . . shocked greatness . . gratified strength . . bored

(A) (B) (C) (D) (E)

interest . . enthralled—NOT OPPOSITE power . . taken—NOT OPPOSITE intensity . . shocked—NOT OPPOSITE greatness . . gratified—NOT OPPOSITE strength . . bored—OPPOSITE

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Critical Reading Strategies

Introduction Before getting into the detailed strategies, I want to say that the most important way to really understand what you’re reading is to get involved with the passage—as if a friend of yours were reading the passage to you and you had to be interested so you wouldn’t slight your friend. When you see the passage on paper it is also a good idea to underline important parts of the passage—which we’ll also go over later in one of the strategies. So many students ask, How do I answer reading comprehension questions? How do I read the passage effectively? Do I look at the questions before reading the passage? Do I underline things in the passage? Do I have to memorize details and dates? How do I get interested and involved in the passage? All these are good questions. They will be answered carefully and in the right sequence.

What Reading Comprehension Questions Ask First of all it is important to know that most reading comprehension questions ask about one of four things: For example, following are some typical question stems. 1. the MAIN IDEA of the passage 2. INFORMATION SPECIFICALLY MENTIONED in the passage 3. INFORMATION IMPLIED (not directly stated) in the passage 4. the TONE or MOOD of the passage

Each lets you immediately know which of the above four things is being asked about. 1. It can be inferred from the passage that . . . (IMPLIED INFORMATION)

2.

According to the author . . . (MAIN IDEA)

3. The passage is primarily concerned with . . . (MAIN IDEA)

4. The author’s statement that . . . (SPECIFIC INFORMATION) 5. Which of the following describes the mood of the passage? (TONE or MOOD) 6. The author implies that . . . (IMPLIED INFORMATION) 7. The use of paper is described in lines 14–16 . . . (SPECIFIC INFORMATION) 8. The main purpose of the passage . . . (MAIN IDEA) 9. The author’s tone is best described as . . . ( TONE or MOOD) 10. One could easily see the author as . . . (IMPLIED INFORMATION)

Getting Involved with the Passage Now, let’s first put aside the burning question, Should I read the questions first, before reading the passage? The answer is NO! If you have in mind the four main question types given above, you will not likely be in for any big surprises. Many questions, when you get to them, will be reassuringly familiar in the way they’re framed and in

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The environmental crisis is the result of success—success in cutting down the mortality of infants (which has given us the population explosion), success in raising farm output sufficiently to prevent mass famine (which has given us contamination by pesticides and chemical fertilizers), success in getting the people out of the tenements of the 19th-century cities and into the greenery and privacy of the single-family home in the suburbs (which has given us urban sprawl and traffic jams). The environmental crisis, in other words, is largely the result of doing too much of the right sort of thing. To overcome the problems that success always creates, one must build on it. But where to start? Cleaning up the environment requires determined, sustained effort with clear targets and deadlines. It requires, above all, concentration of effort. Up to now we have tried to do a little bit of everything— and tried to do it in the headlines—when what we ought to do first is draw up a list of priorities.

their intent. You can best answer them by reading the passage first, allowing yourself to become involved with it. To give you an idea of what I mean, look over the following passage. When you have finished, I’ll show you how you might read it so as to get involved with it and with the author’s intent. Introductor y Passage 1 We should also know that “greed” has little to do with the environmental crisis. The two main causes are population pressures, especially the pressures of large metropolitan populations, and the desire—a highly commendable one—to bring a decent living at the lowest possible cost to the largest possible number of people.

Breakdown and Underlining of Passage Before going over the passage with you, I want to suggest some underlining you might want to make and to show what different parts of the passage refer to. We should also know that “greed” has little to do with the environmental crisis. The two main causes are population pressures, especially the pressures of large metropolitan populations, and the desire—a highly commendable one—to bring a decent living at the lowest possible cost to the largest possible number of people. The environmental crisis is the result of success— success in cutting down the mortality of infants (which has given us the population explosion), success in raising farm output sufficiently to prevent mass famine (which has given us contamination by pesticides and chemical fertilizers), success in getting the people out of the tenements of the 19th-century cities and into the greenery and privacy of the single-family home in the suburbs (which has given us urban sprawl and traffic jams). The environmental crisis, in other words, is largely the result of doing too much of the right sort of thing. To overcome the problems that success always creates, one must build on it. But where to start? Cleaning up the environment requires determined, sustained effort with clear targets and deadlines. It requires above all, concentration of effort. Up to now we have tried to do a little bit of everything—and tried to do it in the headlines—when what we ought to do first is draw up a list of priorities.

Now I’ll go over the passage with you, showing you what might go through your mind as you read. This will let you see how to get involved with the passage, and how this involvement facilitates answering the questions that follow the passage. In many cases, you’ll actually be able to anticipate the questions. Of course, when you are preparing for the SAT, you’ll have to develop this skill so that you do it rapidly and almost automatically. Let’s look at the first sentence:

冧

Sets stage.

冧

This should interest and surprise you.

冧

Examples of success.

冧

Summary of the success examples.

冧

Solutions.

We should also know that “greed” has little to do with the environmental crisis. Immediately you should say to yourself, “So something else must be involved with the environmental crisis.” Read on: The two main causes are population pressures, especially the pressures of large metropolitan populations, and the desire—a highly commendable one—to bring a decent living at the lowest possible cost to the largest possible number of people.

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Now you can say to yourself, “Oh, so population pressures and the desire to help the people in the community caused the environmental crisis.” You should also get a feeling that the author is not really against these causes of the environmental crisis, and that he or she believes that the crisis is in part a side effect of worthwhile efforts and enterprises. Read on:

So you can now see that, in the author’s opinion, making a list of priorities and working on them one at a time, with a target in mind, may get us out of the environmental crisis and still preserve our quality of life.

The environmental crisis is the result of success—success in cutting down the mortality of infants (which has given us the population explosion), success in raising farm output sufficiently to prevent mass famine (which has given us contamination by pesticides and chemical fertilizers), success in getting the people out of the tenements of the 19th-century city and into the greenery and privacy of the single-family home in the suburbs (which has given us urban sprawl and traffic jams).

How to Answer Reading Comprehension Questions Most Effectively

Now you should say to yourself, “It seems that for every positive thing that the author mentions, there is a negative occurrence that leads to the environmental crisis.” Now read the last sentence of this paragraph: The environmental crisis, in other words, is largely the result of doing too much of the right sort of thing.

Now you can say to yourself, “Gee, we wanted to do the right thing, but we created something bad. It looks like you can’t have your cake and eat it, too!” Now you should anticipate that in the next and final paragraph, the author will discuss what may be done to reduce the bad effects that come from the good. Look at the first sentence of the third paragraph: To overcome the problem that success always creates, one must build on it.

Now you can say to yourself, “Well, how?” In fact, in the next sentence the author asks the very question you just asked: But where to start? Read on to find out the author’s answer. Cleaning up the environment requires determined, sustained effort with clear targets and deadlines. It requires, above all, concentration and effort.

So now you can say to yourself, “Oh, so that’s what we need—definite goals, deadlines for reaching those goals, and genuine effort to achieve the goals.” The author then discusses what you may have already thought about: Up to now we have tried to do a little bit of everything . . .

What the author is saying (and you should realize this) is that up to now, we haven’t concentrated on one particular problem at a time. We used “buckshot instead of bullets.” Read on:

—and tried to do it in the headlines—when what we ought to do first is to draw up a list of priorities.

Before we start to answer the questions, let me tell you the best and most effective way of answering passage questions. You should read the question and proceed to look at the choices in the order of Choice A, Choice B, etc. If a choice (such as Choice A) doesn’t give you the definite feeling that it is correct, don’t try to analyze it further. Go on to Choice B. Again, if that choice (Choice B) doesn’t make you feel that it’s the right one, and you really have to think carefully about the choice, go on to Choice C and the rest of the choices and choose the best one. Suppose you have gone through all five choices, and you don’t know which one is correct, or you don’t see any one that stands out as obviously being correct. Then quickly guess or leave the question blank if you wish and go on to the next question. You can go back after you have answered the other questions relating to the passage. But remember, when you return to the questions you weren’t sure of, don’t spend too much time on them. Try to forge ahead on the test. Let’s proceed to answer the questions now. Look at the first question: 1.

This passage assumes the desirability of (A) (B) (C) (D)

using atomic energy to conserve fuel living in comfortable family lifestyles settling disputes peacefully combating cancer and heart disease with energetic research (E) having greater government involvement in people’s daily lives Look at Choice A. That doesn’t seem correct. Now look at Choice B. Do you remember that the author claimed that the environmental crisis is the result of the successful attempt to get people out of their tenements into a better environment? We can only feel that the author assumes this desirability of living in comfortable family lifestyles (Choice B) since the author uses the word success in describing the transition from living in

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tenements to living in single-family homes. Therefore, Choice B is correct. You don’t need to analyze or even consider the other choices, since we have zeroed in on Choice B. Let’s look at Question 2: 2.

According to this passage, one early step in any effort to improve the environment would be to (A) (B) (C) (D) (E)

return to the exclusive use of natural fertilizers put a high tax on profiteering industries ban the use of automobiles in the cities study successful efforts in other countries set up a timetable for corrective actions

Again let’s go through the choices in the order Choice A, Choice B, etc., until we come up with the right choice. Choices A, B, C, and D seem unlikely to be correct. So look at Choice E. We remember that the author said that we should establish clear targets and deadlines to improve the environment. That makes Choice E look like the correct answer. Let’s look at Question 3: 3.

The passage indicates that the conditions which led to overcrowded roads also brought about (A) more attractive living conditions for many people (B) a healthier younger generation (C) greater occupational opportunities (D) the population explosion (E) greater concentration of population pressures

Here we would go back to the part of the passage that discussed overcrowded roads. This is where (second paragraph) the author says that urban sprawl and traffic jams are one result of success in getting people out of tenements to single-family homes. So you can see that Choice A is correct. Again, there is no need to consider other choices, since you should be fairly comfortable with Choice A. Let’s look at Question 4: 4.

It could logically be assumed that the author of this passage would support legislation to (A) ban the use of all pesticides (B) prevent the use of automobiles in the cities (C) build additional conventional power plants immediately (D) organize an agency to coordinate efforts to cope with environmental problems (E) restrict the press coverage of protests led by environmental groups

This is the type of question that asks you to determine what the author would feel about something else,

when you already know something about the author’s sentiments on one particular subject. Choices A, B, and C do not seem correct. But look at Choice D. The author said that the way to get out of the energy crisis is to set targets and deadlines in order to cope with specific problems. The author would therefore probably organize an agency to do this. Choice D is correct. Let’s look at another passage, and what I’m going to tell you is what would be going through my mind as I’m reading it. The more you can get involved with the passage in an “active” and not “passive” way, the faster you’ll read it, and the more you’ll get out of it.

Introductor y Passage 2 Some scraps of evidence bear out those who hold a very high opinion of the average level of culture among the Athenians of the great age. The funeral speech of Pericles is the most famous indication from Athenian literature that its level was indeed high. Pericles was, however, a politician, and he may have been flattering his audience. We know that thousands of Athenians sat hour after hour in the theater listening to the plays of the great Greek dramatists. These plays, especially the tragedies, are at a very high intellectual level throughout. There are no letdowns, no concessions to the lowbrows or to the demands of “realism,” such as the scene of the gravediggers in Hamlet. The music and dancing woven into these plays were almost certainly at an equally high level. Our opera—not Italian opera, not even Wagner, but the restrained, difficult opera of the 18th century—is probably the best modern parallel. The comparison is no doubt dangerous, but can you imagine almost the entire population of an American city (in suitable installments, of course) sitting through performances of Mozart’s Don Giovanni or Gluck’s Orpheus? Perhaps the Athenian masses went to these plays because of a lack of other amusements. They could at least understand something of what went on, since the subjects were part of their folklore. For the American people, the subjects of grand opera are not part of their folklore.

Let’s start reading the passage: Some scraps of evidence bear out those who hold a very high opinion of the average level of culture among the Athenians of the great age.

Now this tells you that the author is going to talk about the culture of the Athenians. Thus the stage is set. Go on reading now: The funeral speech of Pericles is the most famous indication from Athenian literature that its level was indeed high.

At this point you should say to yourself: “That’s interesting, and there was an example of the high level of culture.”

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Read on:

1.

(A) (B) (C) (D) (E)

Pericles was, however, a politician, and he may have been flattering his audience.

Now you can say, “So that’s why those people were so attentive in listening—they were being flattered.” Read on:

2.

3.

At this point you should say to yourself, “That’s strange—it could not have been just flattery that kept them listening hour after hour. How did they do it?” You can almost anticipate that the author will now give examples and contrast what he is saying to our plays and our audiences.

The music and dancing woven into these plays were almost certainly at an equally high level. Our opera, not Italian opera . . . is probably the best modern parallel. The comparison is no doubt dangerous, but can you imagine almost the entire population of an American city . . . sitting through performances of . . .

enjoys Hamlet loves folklore does not understand grand opera seeks a high cultural level lacks entertainment

The author’s attitude toward Greek plays is one of (A) (B) (C) (D) (E)

4.

politicians playwrights opera goers “low brows” gravediggers

The author implies that the average American (A) (B) (C) (D) (E)

We know that thousands of Athenians sat hour after hour in the theater listening to the plays of the great Greek dramatists. These plays, especially the tragedies, are at a very high intellectual level throughout. There are no letdowns, no concessions to the lowbrows or to the demands of “realism”. . .

Read on:

The author seems to question the sincerity of

qualified approval grudging admiration studied indifference partial hostility great respect

The author suggests that Greek plays (A) (B) (C) (D) (E)

made great demands upon their actors flattered their audiences were written for a limited audience were dominated by music and dancing stimulated their audiences

Let’s try to answer them. Your feeling at this point should be, “No, I cannot imagine that. Why is that so?” So you should certainly be interested to find out. Read on: Perhaps the Athenian masses went to these plays because of a lack of other amusements. They could at least understand something of what went on, since the subjects were part of their folklore.

Now you can say, “So that’s why those people were able to listen hour after hour—the material was all part of their folklore!” Read on: For the American people, the subjects . . . are not part of their folklore.

Now you can conclude, “So that’s why the Americans cannot sit through these plays and perhaps cannot understand them—they were not part of their folklore!” Here are the questions that follow the passage:

Question 1: Remember the statement about Pericles? This statement was almost unrelated to the passage since it was not discussed or referred to again. And here we have a question about it. Usually, if you see something that you think is irrelevant in a passage you may be pretty sure that a question will be based on that irrelevancy. It is apparent that the author seems to question the sincerity of politicians (not playwrights) since Pericles was a politician. Therefore Choice A is correct. Question 2: We know that it was implied that the average American does not understand grand opera. Therefore Choice C is correct. Question 3: From the passage, we see that the author is very positive about the Greek plays. Thus the author must have great respect for the plays. Note that the author may not have respect for Pericles, but Pericles was not a playwright; he was a politician. Therefore Choice E (not Choice A) is correct. Question 4: It is certainly true that the author suggests that the Greek plays stimulated their

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audiences. They didn’t necessarily flatter their audiences—there was only one indication of flattery, and that was by Pericles,

who was not a playwright, but a politician. Therefore Choice E (not Choice B) is correct.

Example of Underlinings Some scraps of evidence bear out those who hold a very high ← sets stage opinion of the average level of culture among the Athenians of the great age. The funeral speech of Pericles is the most famous indication from Athenian literature that its level was indeed high. Pericles was, however, a politician, and he may have been ← example flattering his audience. We know that thousands of Athenians sat hour after hour in the theater listening to the plays of the ← qualification great Greek dramatists. These plays, especially the tragedies, are at a very high intellectual level throughout. There are no letdowns, no concessions to the lowbrows or to the demands of “realism,” such as the scene of the gravediggers in HAMLET. ← further The music and dancing woven into these plays were almost examples certainly at an equally high level. Our opera—not Italian opera, not even Wagner, but the restrained, difficult opera of the 18th century—is probably the best modern parallel. The comparison ← comparison is no doubt dangerous, but can you imagine almost the entire population of an American city (in suitable installments, of course) sitting through performances of Mozart’s DON GIOVANNI or Gluck’s ORPHEUS? Perhaps the Athenian masses went to these plays because of a lack of other amusements. They could at least understand something of what went on, since the ← explanation subjects were part of their folklore. For the American people, of previous the subjects of grand opera are not part of their folklore. statements

←

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Now the whole purpose of analyzing this passage the way I did was to show you that if you get involved and interested in the passage, you will not only anticipate many of the questions, but when you answer them you can zero in on the right question choice without having to necessarily analyze or eliminate the wrong choices first. That’s a great time-saver on a standardized test such as the SAT. Now here’s a short passage from which four questions were derived. Let’s see if you can answer them after you’ve read the passage.

1.

(A) (B) (C) (D) (E) 2.

5

*Note: This example also appears in Part 2, The 14 Questions That Can Determine Top College Eligibility.

3.

swim in poisonous water feed on poisonous plants change their feeding habits give off a strange glow take strychnine into their systems

One can most reasonably conclude that plankton are (A) (B) (C) (D) (E)

Introductor y Passage 3* Sometimes the meaning of glowing water is ominous. Off the Pacific Coast of North America, it may mean that the sea is filled with a minute plant that contains a poison of strange and terrible virulence. About four days after this minute plant comes to alter the coastal plankton, some of the fishes and shellfish in the vicinity become toxic. This is because in their normal feeding, they have strained the poisonous plankton out of the water.

Fish and shellfish become toxic when they

minute organisms mussels poisonous fish shellfish fluids

In the context of the passage, the word “virulence” in line 4 means (A) (B) (C) (D) (E)

strangeness color calamity potency powerful odor

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4.

The paragraph preceding this one most probably discussed (A) (B) (C) (D) (E)

phenomena of the Pacific coastline poisons that affect man the culture of the early Indians characteristics of plankton phenomena of the sea EXPLANATORY ANSWER

1. Choice B is correct. See the last three sentences. Fish become toxic when they feed on poisonous plants. Don’t be fooled by using the first sentence, which seemingly leads to Choice A. 2. Choice A is correct. Since we are talking about minute plants (second sentence), it is reasonable to assume that plankton are minute organisms.

3. Choice D is correct. We understand that the poison is very strong and toxic. Thus it is “potent,” virulent. 4. Choice E is correct. Since the second and not the first sentence was about the Pacific Coast, the paragraph preceding this one probably didn’t discuss the phenomena of the Pacific coastline. It would have, if the first sentence—the sentence that links the ideas in the preceding paragraph—were about the Pacific coastline. Now, since we are talking about glowing water being ominous (first sentence), the paragraph preceding the passage is probably about the sea or the phenomena of the sea.

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Summary

So in summary: 1. Make sure that you get involved with the passage. You may even want to select first the passage that interests you most. For example, if you’re interested in science, you may want to choose the science passage first. Just make sure that you make some notation so that you don’t mismark your answer sheet by putting the answers in the wrong answer boxes. 2. Pay attention to material that seems unrelated in the passage—there will probably be a question or two based on that material. 3. Pay attention to the mood created in the passage or the tone of the passage. Here again, especially if the mood is striking, there will probably be a question relating to mood. 4. Don’t waste valuable time looking at the questions before reading the passage.

5. When attempting to answer the questions (after reading the passage) it is sometimes wise to try to figure out the answer before going through the choices. This will enable you to zero in on the correct answer without wasting time with all of the choices. 6. You may want to underline any information in the passages involving dates, specific names, etc., on your test to have as ready reference when you come to the questions. 7. Always try to see the overall attempt of the author of the passage or try to get the main gist of why the passage was being written. Try to get involved by asking yourself if you agree or disagree with the author, etc. Next, the 9 Reading Comprehension Strategies

About the Double-Reading Passages On your SAT you will be given a “double passage” (two separate passages) with about 13 questions. You will also be given a “double paragraph” (two separate paragraphs) with about 4 questions. Some of the questions will be based on only the first passage, some will be based on only the second passage, and some will be based on both passages. Although you may want to read both passages first, then answer all the questions, some of you may find it less anxious to read the first passage, then answer those questions relating to the first passage, then read the second passage and answer those questions relating to the second passage, then finally answer the remaining questions relating to both the passages. By using this approach, since you are reading one passage at a time, the time you would have spent on the second passage could be spent on answering the first set of questions relating to the first passage. This is in case you would have run out of time by reading both passages. The other advantage of this approach is that you do not have to keep both passages in mind at all times when answering the questions. That is, the only time you have to be aware of the content of both passages is when answering only those few questions related to both passages.

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9 Reading Comprehension Strategies

This section of Reading Comprehension Strategies includes several passages. These passages, though somewhat shorter than the passages that appear on the actual SAT and in the 5 SAT Practice Tests in this book, illustrate the general nature of the “real” SAT reading passages. Each of the 9 Reading Comprehension Strategies that follow is accompanied by at least two different passages followed by questions and explanatory answers in order to explain how the strategy is used.

. COMP READ. GY E STRAT

As You Read Each Question, Determine the Type: Main Idea, Detecting Details, Inference, Tone/Mood Here are the 4 major abilities tested in Reading Comprehension questions: 1. Main Idea. Selection of the main thought of a passage; ability to judge the general significance of a passage; ability to select the best title of a passage. 2. Detecting Details. Ability to understand the writer’s explicit statements; to get the literal meaning of what is written; to identify details. 3. Inferential Reasoning. Ability to weave together the ideas of a passage and to see their relationships; to draw correct inferences; to go beyond literal interpretation to the implications of the statements. 4. Tone/Mood. Ability to determine from the passage the tone or mood that is dominant in the passage—humorous, serious, sad, mysterious, etc. EXAMPLE 1

The fight crowd is a beast that lurks in the darkness behind the fringe of white light shed over the first six rows by the incandescents atop the ring, and is not to be trusted with pop bottles or other hardware. 5 People who go to prize fights are sadistic. When two prominent pugilists are scheduled to pummel one another in public on a summer’s evening, men and women file into the stadium in the guise of human beings, and thereafter become a part of a gray thing that squats in 10 the dark until, at the conclusion of the bloodletting, they may be seen leaving the arena in the same guise they wore when they entered.

As a rule, the mob that gathers to see men fight is unjust, vindictive, swept by intense, unreasoning hatreds, 15 proud of its swift recognition of what it believes to be sportsmanship. It is quick to greet the purely phony move of the boxer who extends his gloves to his rival who has slipped or been pushed to the floor, and to reward this stimulating but still baloney gesture with a pattering of 20 hands which indicates the following: “You are a good sport. We recognize that you are a good sport, and we know a sporting gesture when we see one. Therefore we are all good sports, too. Hurrah for us!” The same crowd doesn’t see the same boxer stick his 25 thumb in his opponent’s eye or try to cut him with the laces of his glove, butt him or dig him a low one when the referee

1

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isn’t in a position to see. It roots consistently for the smaller man, and never for a moment considers the desperate psychological dilemma of the larger of the two. It howls with glee at a good finisher making his kill. The Roman hordes were more civilized. Their gladiators asked them whether the final blow should be administered or not. The main attraction at the modern prize fight is the spectacle of a man clubbing a helpless and vanquished opponent into complete insensibility. The referee who stops a bout to save a slugged and punch-drunken man from the final ignominy is hissed by the assembled sportsmen. QUESTIONS

1.

The tone of the passage is chiefly (A) (B) (C) (D) (E)

2.

Which group of words from the passage best indicates the author’s opinion? (A) (B) (C) (D) (E)

3.

disgusted jovial matter-of-fact satiric devil-may-care

“referee,” “opponent,” “finisher” “gladiators,” “slugged,” “sporting gesture” “stimulating,” “hissing,” “pattering” “beast,” “lurks,” “gray thing” “dilemma,” “hordes,” “spectacle”

Apparently, the author believes that boxing crowds find the referee both (A) (B) (C) (D) (E)

gentlemanly and boring entertaining and essential blind and careless humorous and threatening necessary and bothersome EXPLANATORY

1. Choice A is correct. The author is obviously much offended (disgusted) by the inhuman attitude of the crowd watching the boxing match. For example, see these lines: Line 1: “The crowd is a beast.” Line 5: “People who go to prize fights are sadistic.” Lines 1314: “. . . the mob that gathers to see men fight is unjust, vindictive, swept by intense hatreds.” Lines 3031: “The Roman hordes were more civilized.”

2. Choice D is correct. The author’s opinion is clearly one of disgust and discouragement because of the behavior of the fight crowd. Accordingly, you would expect the author to use words that were condemnatory, like “beast,” and gloom-filled words like “lurks” and “gray thing.” To answer this question, you must see relationships between words and feelings. So, we have here an INFERENTIAL REASONING questiontype. 3. Choice E is correct. Lines 2427 show that the referee is necessary: “ The same crowd doesn’t see the same boxer stick his thumb into his opponent’s eye . . . when the referee isn’t in a position to see.” Lines 3537 show that the referee is bothersome: “The referee who stops a bout . . . is hissed by the assembled sportsmen.” To answer this question, the student must have the ability to understand the writer’s specific statements. Accordingly, this is a DETECTING DETAILS type of question. EXAMPLE 2*

Mist continues to obscure the horizon, but above us the sky is suddenly awash with lavender light. At once the geese respond. Now, as well as their cries, a beating roar rolls across the water as if five thousand housewives have taken it into their heads to shake out blankets all at one time. Ten thousand housewives. It keeps up—the invisible rhythmic beating of all those goose wings—for what seems a long time. Even Lonnie is held motionless with suspense. Then the geese begin to rise. One, two, three hundred— then a thousand at a time—in long horizontal lines that unfurl like pennants across the sky. The horizon actually darkens as they pass. It goes on and on like that, flock after flock, for three or four minutes, each new contingent announcing its ascent with an accelerating roar of cries and wingbeats. Then gradually the intervals between flights become longer. I think the spectacle is over, until yet another flock lifts up, following the others in a gradual turn toward the northeastern quadrant of the refuge. Finally the sun emerges from the mist; the mist itself thins a little, uncovering the black line of willows on the other side of the wildlife preserve. I remember to close my mouth—which has been open for some time—and inadvertently shut two or three mosquitoes inside. Only a few straggling geese oar their way across the sun’s red surface. Lonnie wears an exasperated, proprietary expression, as if he had produced and directed the show himself and had just received a bad review. “It would have been better with more light,” he says; “I can’t always guarantee just when they’ll start moving.” I assure him I thought it was a fantastic sight. “Well,” he rumbles, “I guess it wasn’t too bad.”

To answer this question, you must be able to determine the tone that is dominant in the passage. Accordingly, this is a TONE/MOOD type of question. *Note this example also appears in Part 2, Strategy Diagnostic Test for the SAT.

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QUESTIONS

1.

In the descriptive phrase “shake out blankets all at one time” (line 5), the author is appealing chiefly to the reader’s (A) (B) (C) (D) (E)

2.

The mood created by the author is one of (A) (B) (C) (D) (E)

3.

tranquility excitement sadness bewilderment unconcern

The main idea expressed by the author about the geese is that they (A) (B) (C) (D) (E)

4.

background sight emotions thoughts hearing

are spectacular to watch are unpredictable disturb the environment produce a lot of noise fly in large flocks

Judging from the passage, the reader can conclude that (A) (B) (C) (D) (E)

the speaker dislikes nature’s inconveniences the geese’s timing is predictable Lonnie has had the experience before both observers are hunters the author and Lonnie are the same person EXPLANATORY ANSWERS

1.

Choice E is correct. See lines 3–5: “. . . a beating roar rolls across the water . . . shake out blankets all

at one time.” The author, with these words, is no doubt appealing to the reader’s hearing. To answer this question, the reader has to identify those words dealing with sound and noise. Therefore, we have here a DETECTING DETAILS type of question. It is also an INFERENTIAL REASONING question-type in that the “sound” words such as “beating” and “roar” lead the reader to infer that the author is appealing to the auditory (hearing) sense. 2. Choice B is correct. Excitement courses right through this passage. Here are examples: Lines 6–7: “. . . the invisible rhythmic beating of all those goose wings.” Line 8: “Even Lonnie is held motionless with suspense.” Lines 9–10: “Then the geese begin to rise . . . a thousand at a time.” Lines 12–15: “. . . flock after flock . . . roar of cries and wingbeats.” To answer this question, you must determine the dominant tone in this passage. Therefore, we have here a TONE/MOOD question type. 3. Choice A is correct. The word “spectacular” means dramatic, thrilling, impressive. There is considerable action expressed throughout the passage. Sometimes there is a lull—then the action begins again. See lines 16–17: “I think the spectacle is over, until yet another flock lifts up, following the others.” To answer this question, you must have the ability to judge the general significance of the passage. Accordingly, we have here a MAIN IDEA type of question. 4. Choice C is correct. See lines 25–29: “Lonnie wears an exasperated, proprietary expression . . . when they’ll start moving.” To answer this question, you must be able to draw a correct inference. Therefore, we have here an INFERENTIAL REASONING type of question.

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Underline the Key Parts of the Reading Passage* The underlinings will help you to answer questions. Reason: Practically every question will ask you to detect a) the main idea or b) information that is specifically mentioned in the passage or c) information that is implied (not directly stated) in the passage or d) the tone or mood of the passage If you find out quickly what the question is aiming for, you will more easily arrive at the correct answer by referring to your underlinings in the passage. EXAMPLE 1

5

10

15

20

That one citizen is as good as another is a favorite American axiom, supposed to express the very essence of our Constitution and way of life. But just what do we mean when we utter that platitude? One surgeon is not as good as another. One plumber is not as good as another. We soon become aware of this when we require the attention of either. Yet in political and economic matters we appear to have reached a point where knowledge and specialized training count for very little. A newspaper reporter is sent out on the street to collect the views of various passers-by on such a question as “Should the United States defend El Salvador?” The answer of the barfly who doesn’t even know where the country is located, or that it is a country, is quoted in the next edition just as solemnly as that of the college teacher of history. With the basic tenets of democracy—that all men are born free and equal and are entitled to life, liberty, and the pursuit of happiness—no decent American can possibly take issue. But that the opinion of one citizen on a technical subject is just as authoritative as that of another is manifestly absurd. And to accept the opinions of all comers as having the same value is surely to encourage a cult of mediocrity.

The author most probably included the example of the question on El Salvador (lines 11–13) in order to (A) move the reader to rage (B) show that he is opposed to opinion sampling (C) show that he has thoroughly researched his project (D) explain the kind of opinion sampling he objects to (E) provide a humorous but temporary diversion from his main point

3.

The author would be most likely to agree that (A) some men are born to be masters; others are born to be servants (B) the Constitution has little relevance for today’s world (C) one should never express an opinion on a specialized subject unless he is an expert in that subject (D) every opinion should be treated equally (E) all opinions should not be given equal weight EXPLANATORY ANSWERS

Which phrase best expresses the main idea of this passage?

1. Choice B is correct. See lines 1–6: “That one citizen . . . attention of either.” These lines indicate that there is quite a distinction about equality when we are dealing with all the American people.

(A) (B) (C) (D) (E)

2. Choice D is correct. See lines 9–14: “A newspaper reporter . . . college teacher of history.” These lines show that the author probably included the example of the question of El Salvador in order to explain the kind of opinion sampling he objects to.

QUESTIONS

1.

2.

the myth of equality a distinction about equality the essence of the Constitution a technical subject knowledge and specialized training

*Strategy 2 is considered the Master Reading Comprehension Strategy because it can be used effectively in every Reading Comprehension question. However, it is important that you learn the other Reading Comprehension Strategies because they can often be used to double-check your answers.

2

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3. Choice E is correct. See lines 18–21: “But that the opinion . . . to encourage a cult of mediocrity.” Accordingly, the author would be most likely to agree that all opinions should not be given equal weight.

2.

(A) (B) (C) (D) (E)

EXAMPLE 2

5

10

15

20

25

30

She walked along the river until a policeman stopped her. It was one o’clock, he said. Not the best time to be walking alone by the side of a half-frozen river. He smiled at her, then offered to walk her home. It was the first day of the new year, 1946, eight and a half months after the British tanks had rumbled into Bergen-Belsen. That February, my mother turned twenty-six. It was difficult for strangers to believe that she had ever been a concentration camp inmate. Her face was smooth and round. She wore lipstick and applied mascara to her large dark eyes. She dressed fashionably. But when she looked into the mirror in the mornings before leaving for work, my mother saw a shell, a mannequin who moved and spoke but who bore only a superficial resemblance to her real self. The people closest to her had vanished. She had no proof that they were truly dead. No eyewitnesses had survived to vouch for her husband’s death. There was no one living who had seen her parents die. The lack of confirmation haunted her. At night before she went to sleep and during the day as she stood pinning dresses she wondered if, by some chance, her parents had gotten past the Germans or had crawled out of the mass grave into which they had been shot and were living, old and helpless, somewhere in Poland. What if only one of them had died? What if they had survived and had died of cold or hunger after she had been liberated, while she was in Celle* dancing with British officers? She did not talk to anyone about these things. No one, she thought, wanted to hear them. She woke up in the mornings, went to work, bought groceries, went to the Jewish Community Center and to the housing office like a robot.

*Celle is a small town in Germany. QUESTIONS

1.

The policeman stopped the author’s mother from walking along the river because (A) (B) (C) (D) (E)

the river was dangerous it was the wrong time of day it was still wartime it was so cold she looked suspicious

The author states that his mother thought about her parents when she

3.

walked along the river thought about death danced with officers arose in the morning was at work

When the author mentions his mother’s dancing with the British officers, he implies that his mother (A) compared her dancing to the suffering of her parents (B) had clearly put her troubles behind her (C) felt it was her duty to dance with them (D) felt guilty about dancing (E) regained the self-confidence she once had EXPLANATORY ANSWERS

1. Choice B is correct. See lines 1–4: “She walked along . . . offered to walk her home.” The policeman’s telling her that it was not the best time to be walking alone indicates clearly that “it was the wrong time of day.” 2. Choice E is correct. Refer to lines 19–26: “. . . during the day . . . dancing with the British officers.” 3. Choice D is correct. See lines 24–26: “What if they had survived . . . dancing with British officers?”

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3

Look Back at the Passage When in Doubt Sometimes while you are answering a question, you are not quite sure whether you have chosen the correct answer. Often, the underlinings that you have made in the reading passage will help you to determine whether a certain choice is the only correct choice. EXAMPLE 1 15

Despite the many categories of the historian, there are only two ages of man. The first age, the age from the beginnings of recorded time to the present, is the age of the cave man. It is the age of war. It is today. The second age, still only a 5 prospect, is the age of civilized man. The test of civilized man will be represented by his ability to use his inventiveness for his own good by substituting world law for world anarchy. That second age is still within the reach of the individual in our time. It is not a part-time job, however. It 10 calls for total awareness, total commitment.

QUESTION

1.

The title that best expresses the ideas of this passage is (A) (B) (C) (D) (E)

QUESTION

1.

for the consideration of an obol or two. The ballot box was stuffed. How is the glory of the American boss diminished! A vile imitation, he. His methods as old as Time!

The author’s attitude toward the possibility of man’s reaching the age of civilization is one of (A) (B) (C) (D) (E)

limited hope complete despair marked uncertainty untempered complacency extreme anger EXPLANATORY ANSWER

1. Choice A is correct. An important idea that you might have underlined is expressed in lines 8–9: “That second age is still within the reach of the individual in our time.” EXAMPLE 2

All museum adepts are familiar with examples of ostrakoi, the oystershells used in balloting. As a matter of fact, these “oystershells” are usually shards of pottery, conveniently glazed to enable the voter to express his wishes in writing. In 5 the Agora, a great number of these have come to light, bearing the thrilling name, Themistocles. Into rival jars were dropped the ballots for or against his banishment. On account of the huge vote taken on that memorable date, it was to be expected that many ostrakoi would be found, but 10 the interest of this collection is that a number of these ballots are inscribed in an identical handwriting. There is nothing mysterious about it! The Boss was on the job, then as now. He prepared these ballots and voters cast them—no doubt

An Odd Method of Voting Themistocles, an Early Dictator Democracy in the Past Political Trickery—Past and Present The Diminishing American Politician EXPLANATORY ANSWER

1. Choice D is correct. An important idea that you might have underlined is expressed in line 12: “The Boss was on the job, then as now.” EXAMPLE 3

But the weather predictions which an almanac always contains are, we believe, mostly wasted on the farmer. He can take a squint at the moon before turning in. He can “smell” snow or tell if the wind is shifting dangerously east. He can 5 register forebodingly an extra twinge in a rheumatic shoulder. With any of these to go by, he can be reasonably sure of tomorrow’s weather. He can return the almanac to the nail behind the door and put a last stick of wood in the stove. For an almanac, a zero night or a morning’s drifted road—none 10 of these has changed much since Poor Richard wrote his stuff and barns were built along the Delaware. QUESTION

1.

The author implies that, in predicting weather, there is considerable value in (A) (B) (C) (D) (E)

reading the almanac placing the last stick of wood in the stove sleeping with one eye on the moon keeping an almanac behind the door noting rheumatic pains

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Lines 4–6: “He can register forebodingly an extra twinge in a rheumatic shoulder.” These underlinings will reveal that, in predicting weather, the quote in lines 4–6 gives you the correct answer.

EXPLANATORY ANSWER

1. Choice E is correct. Important ideas that you might have underlined are the following Lines 2–3: “He can take a squint at the moon.” Line 3: “He can ‘smell’ snow . . .”


Before You Start Answering the Questions, Read the Passage Carefully A great advantage of careful reading of the passage is that you will, thereby, get a very good idea of what the passage is about. If a particular sentence is not clear to you as you read, then reread that sentence to get a better idea of what the author is trying to say. EXAMPLE 1

The American Revolution is the only one in modern history which, rather than devouring the intellectuals who prepared it, carried them to power. Most of the signatories of the Declaration of Independence were intellectuals. This tradi5 tion is ingrained in America, whose greatest statesmen have been intellectuals—Jefferson and Lincoln, for example. These statesmen performed their political function, but at the same time they felt a more universal responsibility, and they actively defined this responsibility. Thanks to them 10 there is in America a living school of political science. In fact, it is at the moment the only one perfectly adapted to the emergencies of the contemporary world, and one which can be victoriously opposed to communism. A European who follows American politics will be struck by the constant 15 reference in the press and from the platform to this political philosophy, to the historical events through which it was best expressed, to the great statesmen who were its best representatives.

2.

According to the passage, intellectuals who pave the way for revolutions are usually (A) (B) (C) (D) (E)

3.

honored misunderstood destroyed forgotten elected to office

Which statement is true according to the passage? (A) America is a land of intellectuals. (B) The signers of the Declaration of Independence were well educated. (C) Jefferson and Lincoln were revolutionaries (D) Adaptability is a characteristic of American political science. (E) Europeans are confused by American politics. EXPLANATORY ANSWERS

[Underlining important ideas as you are reading this passage is strongly urged.] QUESTIONS

1.


Fathers of the American Revolution Jefferson and Lincoln—Ideal Statesmen The Basis of American Political Philosophy Democracy versus Communism The Responsibilities of Statesmen

1. Choice C is correct. Throughout this passage, the author speaks about the basis of American political philosophy. For example, see lines 4–10: “This tradition is ingrained in America, . . . a living school of political science.” 2. Choice C is correct. See lines 1–3: “The American Revolution is the only one . . . carried them to power.” These lines may be interpreted to mean that intellectuals who pave the way for revolutions—other than the American Revolution—are usually destroyed.

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3. Choice D is correct. The word “adaptability” means the ability to adapt—to adjust to a specified use or situation. Now see lines 10–13: “. . . there is in America . . . opposed to communism.”

QUESTIONS

1.

(A) (B) (C) (D) (E)

EXAMPLE 2

The microscopic vegetables of the sea, of which the diatoms are most important, make the mineral wealth of the water available to the animals. Feeding directly on the diatoms and other groups of minute unicellular algae are the marine 5 protozoa, many crustaceans, the young of crabs, barnacles, sea worms, and fishes. Hordes of small carnivores, the first link in the chain of flesh eaters, move among these peaceful grazers. There are fierce little dragons half an inch long, the sharp-jawed arrowworms. There are gooseberrylike comb 10 jellies, armed with grasping tentacles, and there are the shrimplike euphausiids that strain food from the water with their bristly appendages. Since they drift where the currents carry them, with no power or will to oppose that of the sea, this strange community of creatures and the marine plants 15 that sustain them are called plankton, a word derived from the Greek, meaning wandering. [Underlining important ideas as you are reading this passage is strongly urged.]

According to the passage, diatoms are a kind of

2.

mineral alga crustacean protozoan fish

Which characteristic of diatoms does the passage emphasize? (A) (B) (C) (D) (E)

size feeding habits activeness numerousness cellular structure EXPLANATORY ANSWERS

1. Choice B is correct. See lines 3–5: “Feeding directly on the diatoms . . . minute unicellular algae are the marine protozoa. . . .” These lines indicate that diatoms are a kind of alga. 2. Choice A is correct. See lines 1–4: “The microscopic vegetables of the sea . . . minute unicellular algae . . .” In these lines, the words “microscopic” and “minute” emphasize the small size of the diatoms.


Get the Meanings of “Tough” Words by Using the Context Method

Suppose you don’t know the meaning of a certain word in a passage. Then try to determine the meaning of that word from the context—that is, from the words that are close in position to that word whose meaning you don’t know. Knowing the meanings of difficult words in the passage will help you to better understand the passage as a whole.

EXAMPLE 1

Like all insects, it wears its skeleton on the outside—a marvelous chemical compound called chitin which sheathes the whole of its body. This flexible armor is tremendously tough, light and shatterproof, and resistant to alkali and acid 5 compounds which would eat the clothing, flesh and bones of man. To it are attached muscles so arranged around catapult-like hind legs as to enable the hopper to hop, if so diminutive a term can describe so prodigious a leap as ten or twelve feet—about 150 times the length of the one-inch or so

10

long insect. The equivalent feat for a man would be a casual jump, from a standing position, over the Washington Monument. QUESTIONS

1.

The word “sheathes” (line 2) means (A) (B) (C) (D) (E)

strips provides exposes encases excites

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2.

The word “prodigious” (line 8) means (A) (B) (C) (D) (E)

productive frightening criminal enjoyable enormous

QUESTIONS 1.

(A) (B) (C) (D) (E)

EXPLANATORY ANSWERS

1. Choice D is correct. The words in line 1: “it wears a skeleton on the outside” gives us the idea that “sheathes” probably means “covers” or “encases.” 2. Choice E is correct. See the surrounding words in lines 7–10 “enable the hopper to hop . . . so prodigious a leap as ten or twelve feet—about 150 times the length of the one-inch or so long insect.” We may easily imply that the word “prodigious” means “great in size”; “enormous.” EXAMPLE 2

5

10

15

20

Since the days when the thirteen colonies, each so jealous of its sovereignty, got together to fight the British soldiers, the American people have exhibited a tendency—a genius to maintain widely divergent viewpoints in normal times, but to unite and agree in times of stress. One reason the federal system has survived is that it has demonstrated this same tendency. Most of the time the three coequal divisions of the general government tend to compete. In crises they tend to cooperate. And not only during war. A singular instance of cooperation took place in the opening days of the first administration of Franklin D. Roosevelt, when the harmonious efforts of Executive and Legislature to arrest the havoc of depression brought to term rubber-stamp Congress into the headlines. On the other hand, when in 1937 Roosevelt attempted to bend the judiciary to the will of the executive by “packing” the Supreme Court, Congress rebelled. This frequently proved flexibility—this capacity of both people and government to shift from competition to cooperation and back again as circumstances warrant—suggests that the federal system will be found equal to the very real dangers of the present world situation.

The word “havoc” (line 12) means

2.

possession benefit destruction symptom enjoyment

The word “divergent” (line 4) means (A) (B) (C) (D) (E)

interesting discussed flexible differing appreciated EXPLANATORY ANSWERS

1. Choice C is correct. The prepositional phrase “of depression,” which modifies “havoc,” should indicate that this word has an unfavorable meaning. The only choice that has an unfavorable meaning is Choice C—“destruction.” 2. Choice D is correct. See lines 2–5: “. . . the American people . . . widely divergent viewpoints . . . but to unite and agree in times of stress.” The word “but” in this sentence is an opposite indicator. We may, therefore, assume that a “divergent viewpoint” is a “differing” one from the idea expressed in the words “to unite and agree in times of stress.”

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6

Circle Transitional Words in the Passage There are certain transitional words—also called “bridge” or “key” words—that will help you to discover logical connections in a reading passage. Circling these transitional words will help you to get a better understanding of the passage. Here are examples of commonly used transitional words and what these words may indicate. Transitional Word

although however in spite of rather than nevertheless on the other hand but

Indicating

冧

Key Word moreover besides additionally furthermore in fact

OPPOSITION

QUESTIONS

1.

冧

SUPPORT 2.

Indicating

冧

RESULT

EXAMPLE 1

Somewhere between 1860 and 1890, the dominant emphasis in American literature was radically changed. But it is obvious that this change was not necessarily a matter of conscious concern to all writers. In fact, many writers may seem to have 5 been actually unaware of the shifting emphasis. Moreover, it is not possible to trace the steady march of the realistic emphasis from its first feeble notes to its dominant trumpetnote of unquestioned leadership. The progress of realism is, to change the figure, rather that of a small stream, receiving 10 accessions from its tributaries at unequal points along its course, its progress now and then balked by the sand bars of


Indicating

Key Word therefore consequently accordingly because when so

opposition or the diffusing marshes of error and compromise. Again, it is apparent that any attempt to classify rigidly, as romanticists or realists, the writers of this 15 period is doomed to failure, since it is not by virtue of the writer’s conscious espousal of the romantic or realistic creed that he does much of his best work, but by virtue of that writer’s sincere surrender to the atmosphere of the subject.

Classifying American Writers Leaders in American Fiction The Sincerity of Writers The Values of Realism The Rise of Realism

Which characteristic of writers does the author praise? (A) (B) (C) (D) (E)

their ability to compromise their allegiance to a “school” their opposition to change their awareness of literary trends their intellectual honesty EXPLANATORY ANSWERS

1. Choice E is correct. Note some of the transitional words that will help you to interpret the passage: “but” (line 2); “in fact” (line 4); “moreover” (line 6); “again” (line 13). A better understanding of the passage should indicate to you that the main idea (title)—“The Rise of Realism”—is emphasized throughout the passage. 2. Choice E is correct. See lines 15–18: “. . . since it is not by virtue of . . . but by virtue of the writer’s sincere . . . of the subject.” The transitional word “but” helps us to arrive at the correct answer, which is “their intellectual honesty.”

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EXAMPLE 2

A humorous remark or situation is, furthermore, always a pleasure. We can go back to it and laugh at it again and again. One does not tire of the Pickwick Papers, or of the humor of Mark Twain, any more than the child tires of a 5 nursery tale which he knows by heart. Humor is a feeling and feelings can be revived. But wit, being an intellectual and not an emotional impression, suffers by repetition. A witticism is really an item of knowledge. Wit, again, is distinctly a gregarious quality; whereas humor may abide in 10 the breast of a hermit. Those who live by themselves almost always have a dry humor. Wit is a city, humor a country, product. Wit is the accomplishment of persons who are busy with ideas; it is the fruit of intellectual cultivation and abounds in coffeehouses, in salons, and in literary clubs. But 15 humor is the gift of those who are concerned with persons rather than ideas, and it flourishes chiefly in the middle and lower classes.

QUESTION

1.

It is probable that the paragraph preceding this one discussed the (A) (B) (C) (D) (E)

Pickwick Papers characteristics of literature characteristics of human nature characteristics of humor nature of human feelings EXPLANATORY ANSWER

1. Choice D is correct. See lines 1–2: “A humorous remark or situation is, furthermore, always a pleasure.” The transitional word “furthermore” means “in addition.” We may, therefore, assume that something dealing with humor has been discussed in the previous paragraph.


Don’t Answer a Question on the Basis of Your Own Opinion Answer each question on the basis of the information given or suggested in the passage itself. Your own views or judgments may sometimes conflict with what the author of the passage is expressing. Answer the question according to what the author believes. EXAMPLE 1

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10

15

20

The drama critic, on the other hand, has no such advantages. He cannot be selective; he must cover everything that is offered for public scrutiny in the principal playhouses of the city where he works. The column space that seemed, yesterday, so pitifully inadequate to contain his comments on Long Day’s Journey Into Night is roughly the same as that which yawns today for his verdict on some inane comedy that has chanced to find for itself a numskull backer with five hundred thousand dollars to lose. This state of affairs may help to explain why the New York theater reviewers are so often, and so unjustly, stigmatized as baleful and destructive fiends. They spend most of their professional lives attempting to pronounce intelligent judgments on plays that have no aspiration to intelligence. It is hardly surprising that they lash out occasionally; in fact, what amazes me about them is that they do not lash out more violently and more frequently. As Shaw said of his fellow-critics in the nineties, they are “a culpably indulgent body of men.” Imagine the verbal excoriations that would be inflicted if Lionel Trilling, or someone of comparable eminence, were called on to review five books a month of which three were novelettes composed of criminal confessions. The butchers of Broadway would seem lambs by comparison.

QUESTIONS

1.

In writing this passage, the author’s purpose seems to have been to (A) comment on the poor quality of our plays (B) show why book reviewing is easier than play reviewing (C) point up the opinions of Shaw (D) show new trends in literary criticism (E) defend the work of the play critic

2.

The passage suggests that, as a play, Long Day’s Journey Into Night was (A) (B) (C) (D) (E)

inconsequential worthwhile poorly written much too long pleasant to view

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EXPLANATORY ANSWERS 10

1. Choice E is correct. Throughout the passage, the author is defending the work of the play critic. See, for example, lines 9–14: “This state of affairs . . . plays that have no aspiration to intelligence.” Be sure that you do not answer a question on the basis of your own views. You yourself may believe that the plays presented on the stage today are of poor quality (Choice A) generally. The question, however, asks about the author’s opinion—not yours.

QUESTION

1.

History has long made a point of the fact that the magnificent flowering of ancient civilization rested upon the institution of slavery, which released opportunity at the top of the art and literature which became the glory of antiquity. In a 5 way, the mechanization of the present-day world produces the condition of the ancient in that the enormous development of laborsaving devices and of contrivances which amplify the capacities of mankind affords the base for the

The author’s attitude toward mechanization is one of (A) (B) (C) (D) (E)

2. Choice B is correct. See lines 4–9: “The column space . . . dollars to lose.” You yourself may believe that Long Day’s Journey Into Night is a bad play (Choice A or C or D). But remember—the author’s opinion, not yours, is asked for. EXAMPLE 2

leisure necessary to widespread cultural pursuits. Mechanization is the present-day slave power, with the difference that in the mechanized society there is no group of the community which does not share in the benefits of its inventions.

awe acceptance distrust fear devotion EXPLANATORY ANSWER

1. Choice B is correct. Throughout the passage, the author’s attitude toward mechanization is one of acceptance. Such acceptance on the part of the author is indicated particularly in lines 9–13: “Mechanization is . . . the benefits of its inventions.” You yourself may have a feeling of distrust (Choice C) or fear (Choice D) toward mechanization. But the author does not have such feelings.


8

After Reading the Passage, Read Each Question Carefully Be sure that you read with care not only the stem (beginning) of a question, but also each of the five choices. Some students select a choice just because it is a true statement—or because it answers part of a question. This can get you into trouble. EXAMPLE 1

The modern biographer’s task becomes one of discovering the “dynamics” of the personality he is studying rather than allowing the reader to deduce that personality from documents. If he achieves a reasonable likeness, he need not fear 5 too much that the unearthing of still more material will alter the picture he has drawn; it should add dimension to it, but not change its lineaments appreciably. After all, he has had more than enough material to permit him to reach conclusions and to paint his portrait. With this abundance of 10 material he can select moments of high drama and find episodes to illustrate character and make for vividness. In any event, biographers, I think, must recognize that the writing of a life may not be as “scientific” or as “definitive” as we have pretended. Biography partakes of a large part of 15 the subjective side of man; and we must remember that those who walked abroad in our time may have one appearance for us—but will seem quite different to posterity.

QUESTION

1.

According to the author, which is the real task of the modern biographer? (A) interpreting the character revealed to him by study of the presently available data (B) viewing the life of the subject in the biographer’s own image (C) leaving to the reader the task of interpreting the character from contradictory evidence (D) collecting facts and setting them down in chronological order (E) being willing to wait until all the facts on his subject have been uncovered

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EXPLANATORY ANSWER 10

1. Choice A is correct. See lines 1–7: “ The modern biographer’s task . . . but not change its lineaments appreciably.” The word “dynamics” is used here to refer to the physical and moral forces which exerted influence on the main character of the biography. The lines quoted indicate that the author believes that the real task of the biographer is to study the presently available data. Choice D may also appear to be a correct choice since a biographer is likely to consider his job to be collecting facts and setting them down in chronological order. But the passage does not directly state that a biographer has such a procedure.

The devil-may-care diver who shows great bravado underwater is the worst risk of all. He may lose his bearings in the glimmering dim light which penetrates the sea and become separated from his diving companions. He may dive too deep, too long and suffer painful, sometimes fatal, bends. QUESTION

1.

According to the author, an underwater treasure hunter needs above all, to be (A) (B) (C) (D) (E)

self-reliant adventuresome mentally alert patient physically fit


Although patience is the most important quality a treasure hunter can have, the trade demands a certain amount of courage too. I have my share of guts, but make no boast about ignoring the hazards of diving. As all good divers 5 know, the business of plunging into an alien world with an artificial air supply as your only link to the world above can be as dangerous as stepping into a den of lions. Most of the danger rests within the diver himself.

1. Choice D is correct. See lines 1–3: “Although patience is the most important . . . courage too.” Choice E (“physically fit”) may also appear to be a correct choice since an underwater diver certainly has to be physically fit. Nevertheless, the passage nowhere states this directly.


Increase Your Vocabulary to Boost Your Reading Comprehension Score

1. You can increase your vocabulary tremendously by learning Latin and Greek roots, prefixes, and suffixes. Knowing the meanings of difficult words will thereby help you to understand a passage better. Sixty percent of all the words in our English language are derived from Latin and Greek. By learning certain Latin and Greek roots, prefixes, and suffixes, you will be able to understand the meanings of over 150,000 additional English words. See “Word Building with Roots, Prefixes, and Suffixes” beginning on page 352. 2. This book also includes “A 3,400 SAT Word List” beginning on page 363. This Word List will prove to be a powerful vocabulary builder for you. There are other steps—in addition to the two steps explained above—to increase your vocabulary. Here they are: 3. Take vocabulary tests like the 100 SAT-type “tough word” vocabulary tests beginning on page 415. 4. Read as widely as possible—novels, nonfiction, newspapers, magazines. 5. Listen to people who speak well. Many TV programs have very fine speakers. You can pick up many new words listening to such programs. 6. Get into the habit of using the dictionary often. Why not carry a pocket-size dictionary with you? 7. Play word games—crossword puzzles will really build up your vocabulary.

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EXAMPLE 1

Acting, like much writing, is probably a compensation for and release from the strain of some profound maladjustment of the psyche. The actor lives most intensely by proxy. He has to be somebody else to be himself. But it is all done 5 openly and for our delight. The dangerous man, the enemy of nonattachment or any other wise way of life, is the born actor who has never found his way into the Theater, who never uses a stage door, who does not take a call and then wipe the paint off his face. It is the intrusion of this tempera10 ment into political life, in which at this day it most emphatically does not belong, that works half the mischief in the world. In every country you may see them rise, the actors who will not use the Theater, and always they bring down disaster from the angry gods who like to see 15 mountebanks in their proper place.

2. Choice B is correct. The root “psyche” means the mind functioning as the center of thought, feeling, and behavior. 3. Choice A is correct. The prefix “in” means “into” in this case. The root “trud, trus” means “pushing into”—or entering without being welcome. 4. Choice D is correct. The root “mont” means “to climb.” The root “banc” means a “bench.” A mountebank means literally “one who climbs on a bench.” The actual meaning of mountebank is a quack (faker) who sells useless medicines from a platform in a public place. EXAMPLE 2

QUESTIONS

1.

The meaning of “maladjustment” (line 2) is a (A) (B) (C) (D) (E)

replacement of one thing for another profitable experience in business consideration for the feelings of others disregard of advice offered by other poor relationship with one’s environment

5

10

2.

The meaning of “psyche” (line 3) is (A) (B) (C) (D) (E)

3.

The meaning of “intrusion” (line 9) is (A) (B) (C) (D) (E)

4.

person mind personality psychology physique

entering without being welcome acceptance after considering the facts interest that has developed after a period of time fear as the result of imagination refusing to obey a command

15

20

QUESTIONS

1.

The meaning of “mountebanks” (line 14) is (A) (B) (C) (D) (E)

mountain climbers cashiers high peaks fakers mortals EXPLANATORY ANSWERS

1. Choice E is correct. The prefix “mal” means bad. Obviously a maladjustment is a bad adjustment— that is, a poor relationship with one’s environment.

The American Museum of Natural History has long portrayed various aspects of man. Primitive cultures have been shown through habitat groups and displays of man’s tools, utensils, and art. In more recent years, there has been a tendency to delineate man’s place in nature, displaying his destructive and constructive activities on the earth he inhabits. Now, for the first time, the Museum has taken man apart, enlarged the delicate mechanisms that make him run, and examined him as a biological phenomenon. In the new Hall of the Biology of Man, Museum technicians have created a series of displays that are instructive to a degree never before achieved in an exhibit hall. Using new techniques and new materials, they have been able to produce movement as well as form and color. It is a human belief that beauty is only skin deep. But nature has proved to be a master designer, not only in the matter of man’s bilateral symmetry but also in the marvelous packaging job that has arranged all man’s organs and systems within his skincovered case. When these are taken out of the case, greatly enlarged and given color, they reveal form and design that give the lie to that old saw. Visitors will be sur-prised to discover that man’s insides, too, are beautiful.

The meaning of “bilateral” (line 16) is (A) (B) (C) (D) (E)

2.

biological two-sided natural harmonious technical

The meaning of “symmetry” (line 17) is (A) (B) (C) (D) (E)

simplicity obstinacy sincerity appearance proportion

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STRATEGY SECTION • 147 EXPLANATORY ANSWERS

1. Choice B is correct. The prefix “bi” means “two.” The root “latus” means “side.” Therefore, “bilateral” means “two-sided.”

2. Choice E is correct. The prefix “sym” means “together.” The root “metr” means “measure.” The word “symmetry,” therefore, means “proportion,” “harmonious relation of parts,” “balance.”

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3 Vocabulary Strategies

Introduction Although antonyms (opposites of words) are not on the SAT, it is still important for you to know vocabulary and the strategies to figure out the meanings of words, since there are many questions involving difficult words in all the sections on the Verbal part of the SAT, that is the Sentence Completions and Critical Reading Parts.

ULARY VOCAB GY E STRAT

1

Use Roots, Prefixes, and Suffixes to Get the Meanings of Words

You can increase your vocabulary tremendously by learning Latin and Greek roots, prefixes, and suffixes. Sixty percent of all the words in our English language are derived from Latin and Greek. By learning certain Latin and Greek roots, prefixes, and suffixes, you will be able to understand the meanings of more than 150,000 additional English words. See “Word Building with Roots, Prefixes, and Suffixes” beginning on page 352. and Hot Prefixes and Roots in Appendix A. EXAMPLE 1

EXAMPLE 2

Opposite of PROFICIENT:

Opposite of DELUDE:

(A) (B) (C) (D) (E)

(A) (B) (C) (D) (E)

antiseptic unwilling inconsiderate neglectful awkward

include guide reply upgrade welcome

EXPLANATORY ANSWER

EXPLANATORY ANSWER

Choice E is correct. The prefix PRO means forward, for the purpose of. The root FIC means to make or to do. Therefore, PROFICIENT literally means doing something in a forward way. The definition of proficient is skillful, adept, capable. The antonym of proficient is, accordingly, awkward, incapable.

Choice B is correct. The prefix DE means downward, against. The root LUD means to play (a game). Therefore, DELUDE literally means to play a game against. The definition of delude is to deceive, to mislead. The antonym of delude is accordingly to guide.

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STRATEGY SECTION • 149 EXAMPLE 3

EXAMPLE 6

Opposite of LAUDATORY:

Opposite of RECEDE:

(A) (B) (C) (D) (E)

(A) (B) (C) (D) (E)

vacating satisfactory revoking faultfinding silent

accede settle surrender advance reform

EXPLANATORY ANSWER

EXPLANATORY ANSWER

Choice D is correct. The root LAUD means praise. The suffix ORY means a tendency toward. Therefore, LAUDATORY means having a tendency toward praising someone. The definition of laudatory is praising. The antonym of laudatory is, accordingly, faultfinding.

Choice D is correct. RE back; CED to go; RECEDE to go back— OPPOSITE advance

EXAMPLE 4

Opposite of SUBSTANTIATE: (A) (B) (C) (D) (E)

reveal intimidate disprove integrate assist

Opposite of CIRCUMSPECT: (A) (B) (C) (D) (E)

suspicious overbearing listless determined careless EXPLANATORY ANSWER

EXPLANATORY ANSWER

Choice C is correct. The prefix SUB means under. The root STA means to stand. The suffix ATE is a verb form indicating the act of. Therefore, SUBSTANTIATE literally means to perform the act of standing under. The definition of substantiate is to support with proof or evidence. The antonym is, accordingly, disprove. EXAMPLE 5

Opposite of TENACIOUS: (A) (B) (C) (D) (E)

EXAMPLE 7

changing stupid unconscious poor antagonistic

Choice E is correct. CIRCUM around; SPECT to look or see; CIRCUMSPECT to look all around or make sure that you see everything, careful—OPPOSITE careless EXAMPLE 8

Opposite of MALEDICTION: (A) (B) (C) (D) (E)

sloppiness praise health religiousness proof EXPLANATORY ANSWER

EXPLANATORY ANSWER

Choice A is correct. TEN to hold; TENACIOUS holding—OPPOSITE changing

Choice B is correct. MAL bad; DICT to speak; MALEDICTION to speak badly about—OPPOSITE praise EXAMPLE 9

Opposite of PRECURSORY: (A) (B) (C) (D) (E)

succeeding flamboyant cautious simple cheap

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EXPLANATORY ANSWER

EXPLANATORY ANSWER

Choice A is correct. PRE before; CURS to run; PRECURSORY run before—OPPOSITE succeeding

Choice A is correct. CIRCUM around (like a circle); VENT to come; CIRCUMVENT to come around—OPPOSITE to go the straight route

EXAMPLE 10

Opposite of CIRCUMVENT: (A) (B) (C) (D) (E)

to go the straight route alleviate to prey on one’s emotions scintillate perceive correctly


Pay Attention to the Sound or Feeling of the Word—Whether Positive or Negative, Harsh or Mild, Big or Little, Etc. If the word sounds harsh or terrible, such as “obstreperous,” the meaning probably is something harsh or terrible. If you’re looking for a word opposite in meaning to “obstreperous,” look for a word or words that have a softer sound, such as “pleasantly quiet or docile.” The sense of “obstreperous” can also seem to be negative—so if you’re looking for a synonym, look for a negative word. If you’re looking for an opposite (antonym), look for a positive word. EXAMPLE 1

Opposite of BELLIGERENCY: (A) (B) (C) (D) (E)

pain silence homeliness elegance peace

EXPLANATORY ANSWER

Choice B is correct. Here you can think of the DE in DEGRADES as a prefix that is negative (bad) and means down, and in fact DEGRADE does mean to debase or lower. So you should look for an opposite that would be a word with a positive (good) meaning. The best word from the choices is (B) elevate. EXAMPLE 3

EXPLANATORY ANSWER

Choice E is correct. The word BELLIGERENCY imparts a tone of forcefulness or confusion and means warlike. The opposite would be calmness or peacefulness. The closest choices are choice B or E, with E a little closer to the opposite in tone for the CAPITALIZED word. Of course, if you knew the root BELLI means “war,” you could see the opposite as (E) peace.

Opposite of OBFUSCATION: (A) (B) (C) (D) (E)

illumination irritation conviction minor offense stable environment EXPLANATORY ANSWER

EXAMPLE 2

Opposite of DEGRADE: (A) (B) (C) (D) (E)

startle elevate encircle replace assemble

Choice A is correct. The prefix OB is usually negative, as in obstacle or obliterate, and in fact OBFUSCATE means darken or obscure. So since we are looking for an opposite, you would look for a positive word. Choices A and E are positive, and you should go for the more positive of the two, which is Choice A.

2

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EXAMPLE 4

Opposite of MUNIFICENCE: (A) (B) (C) (D) (E)

disloyalty stinginess dispersion simplicity vehemence

EXPLANATORY ANSWER

Choice A is correct. UNDERSTATE means something said in a restrained or downplayed manner. You see “under” in UNDERSTATE so look for a choice that gives you the impression of something that is “over” as in “over-stated.” The only choice is (A) embroider, which means to embellish. EXAMPLE 7

EXPLANATORY ANSWER

Choice B is correct because MUNIFICENCE means generosity. Many of the words ending in ENCE, like OPULENCE, EFFERVESCENCE, LUMINESCENCE, QUINTESSENCE, etc., represent or describe something big or bright. So the opposite of one of these words would denote something small or dark. You can associate the prefix MUNI with MONEY, as in “municipal bonds,” so the word MUNIFICENCE must deal with money and in a big way. The opposite deals with money in a small way. Choice B fits the bill. EXAMPLE 5

Opposite of DETRIMENT: (A) (B) (C) (D) (E)

recurrence disclosure resemblance enhancement postponement

engage encourage predict dismember misinform EXPLANATORY ANSWER

Choice B is correct. You see “HEART” in DISHEARTEN. The DIS is negative or means “not to,” or “not to have heart,” and dishearten does mean to discourage. So you want to look for a positive word. Choice (B) encourage fits the bill.

Opposite of FIREBRAND:

Choice D is correct. The prefix DE can also mean against and is negative, and DETRIMENT means something that causes damage or loss. So you should look for a positive word. The only one is (E) enhancement. EXAMPLE 6

Opposite of UNDERSTATE: embroider initiate distort pacify reiterate

(A) (B) (C) (D) (E)

EXAMPLE 8

EXPLANATORY ANSWER

(A) (B) (C) (D) (E)

Opposite of DISHEARTEN:

(A) (B) (C) (D) (E)

an intellect one who is charitable one who makes peace a philanthropist one who is dishonest EXPLANATORY ANSWER

Choice C is correct. You see FIRE in FIREBRAND. So think of something fiery or dangerous. The opposite of FIREBRAND must be something that’s calm or safe. The best choice is Choice C, whereas a FIREBRAND is someone who causes trouble.

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3

Use Word Associations to Determine Word Meanings and Their Opposites Looking at the root or part of any capitalized word may suggest an association with another word that looks similar and whose meaning you know. This new word’s meaning may give you a clue as to the meaning of the original word or the opposite in meaning to the original word if you need an opposite. For example, extricate reminds us of the word “extract,” the opposite of which is “to put together.” EXAMPLE 1

Opposite of STASIS: (A) (B) (C) (D) (E)

EXPLANATORY ANSWER

Choice B is correct. Think of MISERY in the word COMMISERATION. Commiseration means the sharing of misery. Choice B is the only appropriate choice.

stoppage reduction depletion fluctuation completion


Choice D is correct. Think of STATIC or STATIONARY. The opposite would be moving or fluctuating since STASIS means stopping or retarding movement. EXAMPLE 2

Opposite of JOCULAR: (A) (B) (C) (D) (E)

unintentional exotic muscular exaggerated serious EXPLANATORY ANSWER

Opposite of APPEASE: (A) (B) (C) (D) (E)

criticize analyze correct incense develop

Choice E is correct. Think of JOKE in the word JOCULAR, which means given to joking. The opposite would be serious.

EXAMPLE 5

EXPLANATORY ANSWER

Choice D is correct. Appease means to placate. Think of PEACE in APPEASE. The opposite would be violent or incense. EXAMPLE 3

Opposite of ELONGATE: (A) (B) (C) (D) (E)

melt wind confuse smooth shorten

Opposite of COMMISERATION: (A) (B) (C) (D) (E)

undeserved reward lack of sympathy unexpected success absence of talent inexplicable danger

EXPLANATORY ANSWER

Choice E is correct. Think of the word LONG in ELONGATE, which means to lengthen. The opposite would be short or shorten.

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EXAMPLE 6

Opposite of SLOTHFUL: (A) (B) (C) (D) (E)

permanent ambitious average truthful plentiful

EXPLANATORY ANSWER

Choice B is correct. LUCID means easily understood or clear; you should think of LUCITE, a clear plastic. The opposite of clear is hard to see through or abstruse. Note: The “ab” in “abstruse” makes Choice B the only negative choice, which is the opposite of the positive word LUCID.

EXAMPLE 9

EXPLANATORY ANSWER

Choice B is correct. Think of SLOTH, a very, very slow animal. So SLOTHFUL, which means lazy or sluggish, must be slow and unambitious. The opposite would be ambitious. EXAMPLE 7

Opposite of POTENT: (A) (B) (C) (D) (E)

imposing pertinent feeble comparable frantic

Opposite of FORTITUDE: (A) (B) (C) (D) (E)

EXPLANATORY ANSWER

timidity conservatism placidity laxness ambition EXPLANATORY ANSWER

Choice A is correct. FORTITUDE means strength in the face of adversity; you should think of FORT or FORTIFY as something strong. The opposite would be weakness or timidity. EXAMPLE 8

Opposite of LUCID: (A) (B) (C) (D) (E)

underlying abstruse luxurious tight general

Choice C is correct. Think of the word POTENTIAL or POWERFUL. To have potential is to have the ability or power to be able to do something. So the opposite would be feeble. You could also have thought of POTENT as a POSITIVE word. The opposite would be a negative word. The only two choices that are negative are choices C and E.

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PA R T 5

MINI–MATH REFRESHER The Most Important Basic Math Rules and Concepts You Need to Know Make sure that you understand each of the following math rules and concepts. It is a good idea to memorize them all. Refer to the section of the Math Refresher (Part 6 starting on page 165) shown in parentheses, e.g., (409), for a complete explanation of each.

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156 • MINI–MATH REFRESHER

Algebra and Arithmetic

(409)

(409)

a(b c) ab ac

(a b)(c d) ac ad bc bd

Example: 5(4 5) 5(4) 5(5) 20 25 45

Example: (2 3)(4 6) (2)(4) (2)(6) (3)(4) (3)(6) 8 12 12 18 10

(a b)2 a2 2ab b2

(409)

(a b)2 a2 2ab b2

(409)

(a b)(a b) a b

(409)

(a b) b a

2

a 1 100 1 101 10 102 100 103 1,000, etc. 0

(429)

Example: 8.6 104 8.6 0 0 0 . 0 1234

2

a2 (a)(a) Example: 22 (2)(2) 4 a3 (a)(a)(a), etc. axay ax y

(429)

ax y ax y a Examples: a3 2 a32 a; a

(429)

Examples: a2 a3 a5; 22 23 25 32 (ax)y axy

(409)

23 2 232 2 2

(429)

Examples: (a3)5 a15; (23)5 215 (429) (ab)x axb x Examples: (2 3)3 23 33; (ab)2 a2b2

(429)

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MINI–MATH REFRESHER • 157

If y2 x then y 兹x苶 (430)

1 a2y y a

Example: If y2 4, then y 兹4苶 2

1 1 Example: 2 3 8 23

Percentage (107)

x x% 100 Example: 5 5% 100

Percentage Problems Examples: (1) What percent of 5 is 2 ?

(107)

x 100 or x (5) 2 100 5x 2 100 5x 200 x 40 Answer 40%

5 2

冢冣

RULE:

“What” becomes x 1 “Percent” becomes 100 “of ” becomes (times) “is” becomes (equals)

(2) 6 is what percent of 24 ? x 24 100 24x 6 100 600 24x 100 4x (dividing both sides by 6) 25 x Answer 25%

6 (107)

(429)

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Equations

(409)

Example: x2 2x 1 0. Solve for x. Procedure: Factor: (x 1)(x 1) 0 x10 x1 Example: x y 1; x y 2. Solve for x and y. Procedure: Add equations: x y1 x y2 2x 0 3 3 Therefore 2x 3 and x 2 3 Substitute x back into one of the equations: 2

(407)

x y1 3 y 1 2 1 y 2

Equalities (402)

abc dd 苶苶苶b苶苶苶苶d 苶苶苶苶c苶苶苶苶d 苶 a苶

347 22 苶苶4苶苶苶苶2苶苶苶苶7苶苶苶苶2苶 3苶苶

Inequalities means greater than, means less than, means greater than or equal to, etc. bc de 苶苶d 苶苶苶苶c苶苶苶苶e苶 b苶苶

(419–425)

43 76 苶苶9苶 1苶1苶苶

54 (6)5 4(6)

5 4 (5) (4)

30 24

54

43 6 7 苶2苶苶苶苶苶4苶 (reversing inequality)

Thus If 2 x 2 then 2 x 2

ab0 Thus a2 b2

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Geometry

(504)

(501)

(504) x y; m n; x m 180; n y 180; y m 180; n x 180

(506)

(506)

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(507)

(501)

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Areas & Perimeters

(304) (306)

(305)

(310)

More on Circles

(527) (526–527)

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(509)

(509)

Here are some right triangles whose relationship of sides you should memorize:

(509)

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Coordinate Geometry

(410–411) (410)

(411)

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PA R T 6

COMPLETE SAT MATH REFRESHER

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166 • COMPLETE SAT MATH REFRESHER

There are many SAT exam takers whose Math background is not quite up to par—probably because their basic Math skills are “rusty” or because they never did do well in their Math classes. For these Math-troubled students, this Math Refresher section will be “manna from heaven.” The pages that follow constitute a complete basic Math course that will help students greatly in preparing for the Math part of the SAT. This Math Refresher offers the following: 1. a systematic review of every Math area covered by the questions in the Math part of the SAT and 2. short review tests throughout the Refresher to check whether the student has grasped the Math principles that he or she has just studied. The review tests will also provide students with valuable reinforcement so that they will remember how to go about solving math problems they would otherwise have difficulty with on the actual SAT. Each of the 8 “Sessions” in this Math Refresher has a review test (“Practice Test”). Almost every review test has 50 questions followed by 50 detailed solutions. All of the solutions for the 8 review tests include a number (or numbers) in parentheses after each solution. The number refers to a specific instructional section where the rules and principles involved in the question are explained simply and clearly. There is another very important purpose that this Math Refresher serves. You will find, after every solution in the Math sections of the 5 SAT Practice Tests in this book, a key to the mathematical principles of this Math Refresher. For example, a solution may direct you to Math Refresher 202, which deals with Distance and Time problems. If you happen to be weak in this mathematical operation, the 202 Math Refresher explanation will immediately clarify for you how to do Distance and Time problems. In other words, for those who are weak in any phase of Basic Math, this invaluable keying system will help you get the right answer to your SAT Math question—and thereby add approximately 10 points to your SAT score.

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COMPLETE SAT MATH REFRESHER • 167

MATH REFRESHER* SESSION 1

*Note: Many of the examples or methods can be done with a calculator, but it is wise for you to know how to solve problems without a calculator.

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Fractions, Decimals, Percentages, Deviations, Ratios and Proportions, Variations, and Comparison of Fractions

Fractions, Decimals, Percentages These problems involve the ability to perform numerical operations quickly and correctly. It is essential that you learn the arithmetical procedures outlined in this section. a 苶. 101. Four different ways to write “a divided by b” are a b, , a : b, b 冄a b 7 苶. Example: 7 divided by 15 is 7 15 7 : 15 15 冄7 15 102. The numerator of a fraction is the upper number and the denominator is the lower number. 8 Example: In the fraction , the numerator is 8 and the denominator is 13. 13 103. Moving a decimal point one place to the right multiplies the value of a number by 10, whereas moving the decimal point one place to the left divides a number by 10. Likewise, moving a decimal point two places to the right multiplies the value of a number by 100, whereas moving the decimal point two places to the left divides a number by 100. Example:

24.35 10 243.5 (decimal point moved to right) 24.35 10 2.435 (decimal point moved to left)

To change a fraction to a decimal, divide the numerator of the fraction by its denominator. 5 Example: Express as a decimal. We divide 5 by 6, obtaining 0.83. 6 5 5 6 0.833 . . . 6

104.

105. To convert a decimal to a fraction, delete the decimal point and divide by whatever unit of 10 the number of decimal places represents. Example: Convert 0.83 to a fraction. First, delete the decimal point. Second, two decimal 83 places represent hundredths, so divide 83 by 100: . 100 83 0.83 100

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106. To change a fraction to a percent, find its decimal form, multiply by 100, and add a percent sign. 3 3 Example: Express as a percent. To convert to a decimal, divide 3 by 8, which gives 8 8 us 0.375. Multiply 0.375 by 100 gives us 37.5%. 3 3 38 .375 8 .375 100 37.5% 107. 100.

To change a percent to a fraction, drop the percent sign and divide the number by

Example: Express 17% as a fraction. Dropping the % sign gives us 17, and dividing by 17 100 gives us . 100 108. To reduce a fraction, divide the numerator and denominator by the largest number that divides them both evenly. 10 2 Example: Reduce . Dividing both the numerator and denominator by 5 gives us . 15 3 12 Example: Reduce . The largest number that goes into both 12 and 36 is 12. Reducing 36 1 1冫2 1 the fraction, we have . 3冫6 3 3 Note: In both examples, the reduced fraction is exactly equal to the original fraction: 2 10 12 1 and . 3 15 36 3 109. To add fractions with like denominators, add the numerators of the fractions, keeping the same denominator. 1 2 3 6 Example: . 7 7 7 7 110. To add fractions with different denominators, you must first change all of the fractions to equivalent fractions with the same denominators. STEP 1. Find the lowest (or least) common denominator, the smallest number divisible by all of the denominators. 1 1 5 Example: If the fractions to be added are , , and , then the lowest common denomi3 4 6 nator is 12, because 12 is the smallest number that is divisible by 3, 4, and 6. STEP 2. Convert all of the fractions to equivalent fractions, each having the lowest common denominator as its denominator. To do this, multiply the numerator of each fraction by the number of times that its denominator goes into the lowest common denominator. The product of this multiplication will be the new numerator. The denominator of the equivalent fractions will be the lowest common denominator. (See Step 1 above.) 1 1 5 1 4 Example: The lowest common denominator of , , and is 12. Thus, , because 3 4 6 3 12 1 3 12 divided by 3 is 4, and 4 times 1 4. , because 12 divided by 4 is 3, and 3 times 4 12 5 10 1 3. because 12 divided by 6 is 2, and 2 times 5 10. 6 12 Now add all of the equivalent fractions by adding the numerators. 10 17 4 3 Example: 12 12 12 12

STEP 3.

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STEP 4.

Reduce the fraction if possible, as shown in Section 108.

4 2 8 Example: Add , and . The lowest common denominator is 15 because 15 is the 5 3 15 4 12 2 smallest number that is divisible by 5, 3, and 15. Then, is equivalent to ; is equivalent 5 15 3 10 12 10 30 8 8 8 to ; and remains as . Adding these numbers gives us . Both 30 15 15 15 15 15 15 15 2 and 15 are divisible by 15, giving us , or 2. 1 111.

To multiply fractions, follow this procedure:

STEP 1. To find the numerator of the product, multiply all the numerators of the fractions being multiplied. STEP 2. To find the denominator of the answer, multiply all of the denominators of the fractions being multiplied. STEP 3.

Reduce the product.

5 2 52 10 Example: . Reduce by dividing both the numerator and denomi7 15 7 15 105 10 2 nator by 5, the common factor. . 105 21 112.

To divide fractions, follow this procedure:

STEP 1. Invert the divisor. That is, switch the positions of the numerator and denominator in the fraction you are dividing by. STEP 2.

Replace the division sign with a multiplication sign.

STEP 3.

Carry out the multiplication indicated.

STEP 4.

Reduce the product.

3 7 7 8 Example: Find . Inverting , the divisor, gives us . Replacing the division sign 4 8 8 7 3 8 3 8 with a multiplication sign gives us . Carrying out the multiplication gives us 4 7 4 7 24 24 6 . The fraction may then be reduced to by dividing both the numerator and the 28 28 7 denominator by 4. 113.

To multiply decimals, follow this procedure:

STEP 1. Disregard the decimal point. Multiply the factors (the numbers being multiplied) as if they were whole numbers. STEP 2. In each factor, count the number of digits to the right of the decimal point. Find the total number of these digits in all the factors. In the product start at the right and count to the left this (total) number of places. Put the decimal point there. Example: Multiply 3.8 4.01. First, multiply 38 and 401, getting 15,238. There is a total of 3 digits to the right of the decimal points in the factors. Thus, the decimal point in the product is placed 3 units to the left of the digit farthest to the right (8). 3.8 4.01 15.238 Example: 0.025 3.6. First, multiply 25 36, getting 900. In the factors, there is a total of 4 digits to the right of the decimal points; therefore, in the product, we place the decimal point 4 units to the left of the digit farthest to the right in 900. However, there are only 3 digits in the product, so we add a 0 to the left of the 9, getting 0900. This makes it possible to place the decimal point correctly, thus: .0900. From this example, we can make up the rule

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that in the product we add as many zeros as are needed to provide the proper number of digits to the left of the digit farthest to the right. 114.

To find a percent of a given quantity:

STEP 1.

Replace the word “of” with a multiplication sign.

STEP 2. Convert the percent to a decimal: drop the percent sign and divide the number by 100. This is done by moving the decimal point two places to the left, adding zeros where necessary. Examples: 30% 0.30. STEP 3.

2.1% 0.021.

78% 0.78.

Multiply the given quantity by the decimal.

Example: Find 30% of 200. 30 % of 200 30 % 200 0.30 200 60.00

Deviations Estimation problems arise when dealing with approximations, that is, numbers that are not mathematically precise. The error, or deviation, in an approximation is a measure of the closeness of that approximation. 115. Absolute error, or absolute deviation, is the difference between the estimated value and the real value (or between the approximate value and the exact value). Example: If the actual value of a measurement is 60.2 and we estimate it as 60, then the absolute deviation (absolute error) is 60.2 60 0.2. 116. Fractional error, or fractional deviation, is the ratio of the absolute error to the exact value of the quantity being measured. Example: If the exact value is 60.2 and the estimated value is 60, then the fractional error is 0.2 60.2 60 1 . 60.2 60.2 301 117. Percent error, or percent deviation, is the fractional error expressed as a percent. (See Section 106 for the method of converting fractions to percents.) 118. Many business problems, including the calculation of loss, profit, interest, and so forth, are treated as deviation problems. Generally, these problems concern the difference between the original value of a quantity and some new value after taxes, after interest, etc. The following chart shows the relationship between business and estimation problems.

Business Problems

Estimation Problems

original value

exact value

new value

approximate value

net profit net loss net interest

冧

absolute error

fractional profit fractional loss fractional interest percent profit percent loss percent interest

冧

冧

fractional error

percent error

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Example: An item that originally cost $50 is resold for $56. Thus the net profit is $56 $50 $6 3 $56 $50 $6. The fractional profit is . The percent profit is equal to $50 $50 25 3 the percent equivalent of , which is 12%. 25 119. When there are two or more consecutive changes in value, remember that the new value of the first change becomes the original value of the second; consequently, successive fractional or percent changes may not be added directly. Example: Suppose that a $100 item is reduced by 10 % and then by 20 %. The first reduction puts the price at $90 (10 % of $100 $10; $100 $10 $90). Then, reducing the $90 (the new original value) by 20 % gives us $72 (20 % of $90 $18; $90 $18 $72). Therefore, it is not correct to simply add 10% and 20 % and then take 30% of $100.

Ratios and Proportions 120. A proportion is an equation stating that two ratios are equal. For example, 3 : 2 9 : x and 7 : 4 a : 15 are proportions. To solve a proportion: a STEP 1. First change the ratios to fractions. To do this, remember that a : b is the same as , b 1 7 a or 1 : 2 is equivalent to , or 7 : 4 a : 15 is the same as . 2 4 15 STEP 2. Now cross-multiply. That is, multiply the numerator of the first fraction by the denominator of the second fraction. Also multiply the denominator of the first fraction by the numerator of the second fraction. Set the first product equal to the second. This rule is sometimes stated as “ The product of the means equals the product of the extremes.” 3 9 Example: When cross-multiplying in the equation , we get 3 y 2 9, or 2 y 3y 18. a 4 When we cross-multiply in the equation , we get 8a 8. 2 8 STEP 3.

Solve the resulting equation. This is done algebraically.

Example: Solve for a in the proportion 7 : a 6 : 18. 7 6 Change the ratios to the fractional relation . Cross-multiply: 7 18 6 a, or a 18 126 6a. Solving for a gives us a 21. 121. In solving proportions that have units of measurement (feet, seconds, miles, etc.), each ratio must have the same units. For example, if we have the ratio 5 inches : 3 feet, we must convert the 3 feet to 36 inches and then set up the ratio 5 inches : 36 inches, or 5 : 36. We might wish 1 1 to convert inches to feet. Noting that 1 inch foot, we get 5 inches : 3 feet 5 feet : 3 feet 12 12 5 feet : 3 feet. 12

冢冣

Example: On a blueprint, a rectangle measures 6 inches in width and 9 inches in length. If the actual width of the rectangle is 16 inches, how many feet are there in the length? Solution: We set up the proportions, 6 inches : 9 inches 16 inches : x feet. Since x feet is equal to 12x inches, we substitute this value in the proportion. Thus, 6 inches : 9 inches 16 inches : 12x inches. Since all of the units are now the same, we may work with the numbers 6 16 alone. In fractional terms we have . Cross-multiplication gives us 72x 144, 9 12x and solving for x gives us x 2. The rectangle is 2 feet long.

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Variations 122. In a variation problem, you are given a relationship between certain variables. The problem is to determine the change in one variable when one or more of the other variables changes. Example: In the formula A bh, if b doubles and h triples, what happens to the value of A? STEP 1. Express the new values of the variables in terms of their original values, i.e., b 2b and h 3h. STEP 2. Substitute these values in the formula and solve for the desired variable: A b h (2b)(3h) 6bh. STEP 3. Express this answer in terms of the original value of the variable, i.e., since the new value of A is 6bh, and the old value of A was bh, we can express this as Anew 6Aold. The new value of the variable is expressed with a prime mark and the old value of the variable is left as it was. In this problem the new value of A would be expressed as A and the old value as A. A 6A. Example: If V e3 and e is doubled, what happens to the value of V ? Solution: Replace e with 2e. The new value of V is (2e)3. Since this is a new value, V becomes V . Thus V (2e)3, or 8e3. Remember, from the original statement of the problem, that V e3. Using this, we may substitute V for e3 found in the equation V 8e3. The new equation is V 8V. Therefore, the new value of V is 8 times the old value.

Comparison of Fractions In fraction comparison problems, you are given two or more fractions and are asked to arrange them in increasing or decreasing order, or to select the larger or the smaller. The following rules and suggestions will be very helpful in determining which of two fractions is greater. 123. If fractions A and B have the same denominators, and A has a larger numerator, then fraction A is larger. (We are assuming here, and for the rest of this Refresher Session, that numerators and denominators are positive.) 56 53 Example: is greater than because the numerator of the first fraction is greater than 271 271 the numerator of the second. 124. If fractions A and B have the same numerator, and A has a larger denominator, then fra ction A is smaller. 37 37 Example: is smaller than . 256 254 125. If fraction A has a larger numerator and a smaller denominator than fraction B, then fraction A is larger than B. 6 4 Example: is larger than . (If this does not seem obvious, compare both fractions 11 13 6 with .) 13 126. Another method is to convert all of the fractions to equivalent fractions. To do this follow these steps: STEP 1. First find the lowest common denominator of the fractions. This is the smallest number that is divisible by all of the denominators of the original fractions. See Section 108 for the method of finding lowest common denominators.

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STEP 2. 127.

The fraction with the greatest numerator is the largest fraction.

Still another method is the conversion to approximating decimals.

5 7 Example: To compare and , we might express both as decimals to a few places of 9 11 5 7 7 accuracy: is approximately equal to 0.555, while is approximately equal to 0.636, so 9 11 11 is obviously greater. To express a fraction as a decimal, divide the numerator by the denominator. If all of the fractions being compared are very close in value to some easy-to-work-with 1 number, such as or 5, you may subtract this number from each of the fractions without 2 changing this order. 128.

151 328 Example: To compare with we notice that both of these fractions are approxi75 163 150 326 mately equal to 2. If we subtract 2 (that is and , respectively) from each, we 75 163 151 1 2 1 2 2 get and , respectively. Since (or ) exceeds , we see that must also 75 75 163 75 150 163 328 exceed . 163 1 Solution: We notice that both these numbers are close to . 4 An alternative method of comparing fractions is to change the fractions to their decimal equivalents and then compare the decimals. (See Section 104.) The student would weigh the relative amount of work and difficulty involved in each method when he faces each problem. Quick Way of Comparing Fractions 3 7 Example: Which is greater, or ? 8 18 Procedure:

Multiply the 18 by the 3. We get 54. Put the 54 on the left side. 54 Now multiply the 8 by the 7. We get 56. Put the 56 on the right side. 54

56

7 Since 56 54 and 56 is on the right side, the fraction (which was also originally on the 18 3 right side) is greater than the fraction (which was originally on the left side). 8 1 1 Example: If y x, which is greater, or ? (x and y are positive numbers). x y Procedure:

Multiply y by 1. We get y. Put y on the left: y

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Multiply x by 1. We get x. Put x on the right side. y x 1 1 Since y x (given), x (which was originally on the left) is greater than y (which was originally on the right). Example: Which is greater?

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Practice Test 1 Fractions, Decimals, Percentages, Deviations, Ratios and Proportions, Variations, and Comparison of Fractions Correct answers and solutions follow each test. 1.

A

B

C

D

E

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1.

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Which of the following answers is the sum of the following numbers: 1 21 1 2, , 3.350, ? 2 4 8 (A) (B) (C) (D) (E)

2.

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D

E

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2.

A chemist was preparing a solution that should have included 35 milligrams of a chemical. If she actually used 36.4 milligrams, what was her percentage error (to the nearest 0.01%)? (A) (B) (C) (D) (E)

3.

4.

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E

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3.

4.

8.225 9.825 10.825 11.225 12.350

0.04% 0.05% 1.40% 3.85% 4.00%

A retailer buys a radio from the wholesaler for $75.00. He then marks up the price by 1 and sells it at a discount of 20 %. What was his profit on the radio (to the nearest cent)? 3 (A) $5.00 (B) $6.67 (C) $7.50 (D) $10.00 (E) $13.33 1 On a blueprint, inch represents 1 foot. If a window is supposed to be 56 inches wide, 4 how wide would its representation on the blueprint be? 1 (A) 1 inches 6 2 (B) 4 inches 3 1 (C) 9 inches 3 (D) 14 inches 2 (E) 18 inches 3

5.

A

B

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D

E

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5.

If the radius of a circle is increased by 50 %, what will be the percent increase in the circumference of the circle? (Circumference 2p r) (A) (B) (C) (D) (E)

25 % 50 % 100 % 150 % 225 %

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6.

7.

A

B

C

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E

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6.

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Which of the following fractions is the greatest? 403 (A) 134 79 (B) 26 527 (C) 176 221 (D) 73 99 (E) 34

7.

A store usually sells a certain item at a 40 % profit. One week the store has a sale, during which the item is sold for 10 % less than the usual price. During the sale, what is the percent profit the store makes on each of these items? (A) (B) (C) (D) (E)

8.

9.

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B

C

D

E

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8.

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4% 14 % 26 % 30 % 36 %

What is 0.05 percent of 6.5? (A) 0.00325 (B) 0.013 (C) 0.325 (D) 1.30 (E) 130.0

9.

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What is the value of

1 1 1 1 3 3 3 3 2 4 4 2? 1 4 2

1 (A) 1 2 1 (B) 2 4 (C) 3 1 (D) 3 4 3 (E) 3 8 10.

A

B

C

D

E

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10.

If 8 men can chop down 28 trees in one day, how many trees can 20 men chop down in one day? (A) (B) (C) (D) (E)

28 trees 160 trees 70 trees 100 trees 80 trees

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11.

A

B

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D

E

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11.

3 15 7 What is the product of the following fractions: , , ? 100 49 9 215 (A) 44,100 1 (B) 140 1 (C) 196 25 (D) 158 3 (E) 427

12.

A

B

C

D

E

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12.

In reading a thermometer, Mr. Downs mistakenly observed a temperature of 72° instead of 77°. What was his percentage error (to the nearest hundredth of a percent)? (A) (B) (C) (D) (E)

13.

A

B

C

D

E

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13.

A businessman buys 1,440 dozen pens at $2.50 a dozen and then sells them at a price of 25¢ apiece. What is his total profit on the lot of pens? (A) (B) (C) (D) (E)

14.

A

B

C

D

E

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14.

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15.

$60.00 $72.00 $720.00 $874.00 $8740.00

On a map, 1 inch represents 1,000 miles. If the area of a country is actually 16 million square miles, what is the area of the country’s representation on the map? (A) (B) (C) (D) (E)

15.

6.49 % 6.50 % 6.64 % 6.94 % 6.95 %

4 square inches 16 square inches 4,000 square inches 16,000 square inches 4,000,000 square inches

1 The formula for the volume of a cone is V pr 2h. If the radius (r) is doubled and 3 the height (h) is divided by 3, what will be the ratio of the new volume to the original volume? (A) (B) (C) (D) (E)

2:3 3:2 4:3 3:4 None of these.

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16.

A

B

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E

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16.

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Which of the following fractions has the smallest value: 34.7 (A) 163 125 (B) 501 173 (C) 700 10.9 (D) 42.7 907 (E) 3,715

17.

A

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D

E

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17.

Mr. Cutler usually makes a 45% profit on every radio he sells. During a sale, he reduces his margin of profit to 40%, while his sales increase by 10%. What is the ratio of his new total profit to the original profit? (A) (B) (C) (D) (E)

18.

19.

A

B

C

D

E

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18.

What is 1.3 percent of 0.26? (A) (B) (C) (D) (E)

19.

1:1 9:8 9 : 10 11 : 10 44 : 45

0.00338 0.00500 0.200 0.338 0.500

47 10 What is the average of the following numbers: 3.2, , ? 12 3 (A) 3.55 10 (B) 3 103 (C) 30 209 (D) 60 1,254 (E) 120

20.

A

B

C

D

E

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20.

If it takes 16 faucets 10 hours to fill 8 tubs, how long will it take 12 faucets to fill 9 tubs? (A) (B) (C) (D) (E)

10 hours 12 hours 13 hours 14 hours 15 hours

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21.

A

B

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E

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21.

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If the 8 % tax on a sale amounts to 96¢, what is the final price (tax included) of the item? (A) (B) (C) (D) (E)

22.

A

B

C

D

E

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22.

In a certain class, 40% of the students are girls, and 20% of the girls wear glasses. What percent of the children in the class are girls who wear glasses? (A) (B) (C) (D) (E)

23.

24.

A

B

C

D

E

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23.

6% 8% 20 % 60 % 80 %

What is 1.2 % of 0.5? (A) (B) (C) (D) (E)

24.

$1.20 $2.16 $6.36 $12.00 $12.96

0.0006 0.006 0.06 0.6 6.0

Which of the following quantities is the largest? 275 (A) 369 134 (B) 179 107 (C) 144 355 (D) 476 265 (E) 352

25.

A

B

C

D

E

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25.

If the length of a rectangle is increased by 120 %, and its width is decreased by 20%, what happens to the area of the rectangle? (A) (B) (C) (D) (E)

26.

A

B

C

D

E

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26.

It decreases by 4 %. It remains the same. It increases by 24 %. It increases by 76 %. It increases by 100 %.

A merchant buys an old carpet for $25.00. He spends $15.00 to have it restored to good condition and then sells the rug for $50.00. What is the percent profit on his total investment? (A) (B) (C) (D) (E)

20 % 25 % 40 % 66 2/3 % 100 %

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27.

28.

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27.

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Of the following sets of fractions, which one is arranged in decreasing order? 5 3 2 7 (A) , , , , 9 11 5 3 2 3 5 7 (B) , , , , 3 5 11 9 3 5 10 7 (C) , , , , 5 9 11 13 10 2 3 7 (D) , , , , 13 3 11 5 (E) None of these.

28.

If the diameter of a circle doubles, the circumference of the larger circle is how many times the circumference of the original circle? (Circumference pd) (A) (B) (C) (D) (E)

29.

A

B

C

D

E

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29.

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30.

A

B

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D

E

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31.

6.7 % 7.1 % 12.5 % 53.6 % 56.8 %

A salesman bought 2 dozen television sets at $300 each. He sold two-thirds of them at a 25% profit but was forced to take a 30 % loss on the rest. What was his total profit (or loss) on the television sets? (A) (B) (C) (D) (E)

31.

p 2p 1 2 4

The scale on a set of plans is 1 : 8. If a man reads a certain measurement on the plans as 5.6, instead of 6.0, what will be the resulting approximate percent error on the fullsize model? (A) (B) (C) (D) (E)

30.

10 13 10 13 2 3 5 9

a loss of $200 a loss of $15 no profit or loss a gain of $20 a gain of $480

1 1 1 1 The sum of , , , and is: 2 3 8 15 9 (A) 8 16 (B) 15 41 (C) 40 65 (D) 64 121 (E) 120

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32.

A

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32.

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2 What is % of 90? 3 (A) (B) (C) (D) (E)

33.

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33.

A man borrows $360. If he pays it back in 12 monthly installments of $31.50, what is his interest rate? (A) (B) (C) (D) (E)

34.

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D

E

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34.

A

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E

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35.

1.5 % 4.5 % 10 % 5% 7.5 %

A merchant marks a certain lamp up 30 % above original cost. Then he gives a customer a 15 % discount. If the final selling price of the lamp was $86.19, what was the original cost? (A) (B) (C) (D) (E)

35.

0.006 0.06 0.6 6.0 60

$66.30 $73.26 $78.00 $99.12 $101.40

1 In a certain recipe, 2 cups of flour are called for to make a cake that serves 6. If Mrs. 4 Jenkins wants to use the same recipe to make a cake for 8, how many cups of flour must she use? 1 (A) 2 cups 3 3 (B) 2 cups 4 (C) 3 cups 3 (D) 3 cups 8 (E) 4 cups

36.

A

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D

E

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36.

If 10 men can survive for 24 days on 15 cans of rations, how many cans will be needed for 8 men to survive for 36 days? (A) (B) (C) (D) (E)

15 cans 16 cans 17 cans 18 cans 19 cans

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37.

A

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37.

1 1 If, on a map, inch represents 1 mile, how long is a border whose representation is 1 15 2 feet long? 1 (A) 2 miles 30 1 (B) 5 miles 15 4 (C) 12 miles 5 3 (D) 25 miles 5 1 (E) 51 miles 5

38.

39.

40.

A

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38.

In the formula e hf, if e is doubled and f is halved, what happens to the value of h? (A) (B) (C) (D) (E)

39.

Which of the following expresses the ratio of 3 inches to 2 yards? (A) (B) (C) (D) (E)

40.

A

B

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D

E

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42.

2:1 3:1 3:2 3:4 4:3

1 13 4 What is the lowest common denominator of the following set of fractions: , , , 6 27 5 3 2 , ? 10 15 (A) (B) (C) (D) (E)

42.

3:2 3:9 3 : 12 3 : 24 3 : 72

If it takes Mark twice as long to earn $6.00 as it takes Carl to earn $4.00, what is the ratio of Mark’s pay per hour to Carl’s pay per hour? (A) (B) (C) (D) (E)

41.

h remains the same. h is doubled. h is divided by 4. h is multiplied by 4. h is halved.

27 54 135 270 None of these.

The average grade on a certain examination was 85. Ralph, on the same examination, scored 90. What was Ralph’s percent deviation from the average score (to the nearest tenth of a percent)? (A) (B) (C) (D) (E)

5.0 % 5.4 % 5.5 % 5.8 % 5.9 %

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43.

44.

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43.

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Successive discounts of 20% and 12% are equivalent to a single discount of: (A) (B) (C) (D) (E)

44.

1 1 On a blueprint of a park, 1 foot represents mile. If an error of inch is made in 2 2 reading the blueprint, what will be the corresponding error on the actual park? (A) (B) (C) (D) (E)

45.

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45.

16.0 % 29.6 % 31.4 % 32.0 % 33.7 %

110 feet 220 feet 330 feet 440 feet None of these.

If the two sides of a rectangle change in such a manner that the rectangle’s area remains constant, and one side increases by 25%, what must happen to the other side? (A) It decreases by 20% (B) It decreases by 25% 1 (C) It decreases by 33% 3 (D) It decreases by 50% (E) None of these.

46.

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46.

Which of the following fractions has the smallest value? 6043 (A) 2071 4290 (B) 1463 5107 (C) 1772 8935 (D) 2963 8016 (E) 2631

47.

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47.

A certain company increased its prices by 30 % during 2003. Then, in 2004, it was forced to cut back its prices by 20 %. What was the net change in price? (A) (B) (C) (D) (E)

4% 2% 2% 4% 0%

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48.

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48.

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What is 0.04 %, expressed as a fraction? 2 (A) 5 1 (B) 25 4 (C) 25 1 (D) 250 1 (E) 2,500

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49.

What is the value of the fraction 16 12 88 34 66 21 79 11 89 ? 25 (A) (B) (C) (D) (E)

50.

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50.

15.04 15.44 16.24 16.64 None of these.

If coconuts are twice as expensive as bananas, and bananas are one-third as expensive as grapefruits, what is the ratio of the price of one coconut to one grapefruit? (A) (B) (C) (D) (E)

2:3 3:2 6:1 1:6 None of these.

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2pr 2p (1.5) r (1.5) 2p r. Remembering that C 2pr, we get that C (1.5) C. Since the new circumference is 1.5 times the original, there is an increase of 50 %. (122)

Answer Key for Practice Test 1 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

D E A A B B C A C C B A C

14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.

B C A E A D E E B B E D B

27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38.

D D A E C C D C C D D D

39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.

E D D E B A A C D E D A

Answers and Solutions for Practice Test 1 1.

Choice D is correct. First, convert the fractions to decimals, as the final answer must be expressed in decimals: 2.500 5.250 3.350 0.125 11.225. (104, 109)

2.

Choice E is correct. This is an estimation problem. Note that the correct value was 35, not 36.4. Thus the real value is 35 mg and the estimated value is 36.4 mg. Thus, percent error is equal to (36.4 35) 35, or 0.04, expressed as a percent, which is 4%. (117)

3.

4.

Choice A is correct. This is a business problem. First, the retailer marks up the wholesale price by 1 1 , so the marked-up price equals $75 (1 ), or 3 3 $100; then it is reduced 20% from the $100 price, leaving a final price of $80. Thus, the net profit on the radio was $5.00. (118) Choice A is correct. Here we have a proportion 1 problem: length on blueprint: actual length 4 inch; 1 foot. The second ratio is the same as 1 : 48 because 1 foot 12 inches. In the problem the actual length is 56 inches, so that if the length on the blueprint equals x, we have the proportion 56 x 1 x : 56 1 : 48; . 48x 56; so x , or 48 56 48 1 (120) 1 inches. 6

5. Choice B is correct. Since C 2pr (where r is the

radius of the circle, and C is its circumference), the new value of r, r , is (1.5) r since r is increased by 50 %. Using this value of r , we get the new C, C

6.

Choice B is correct. In this numerical comparison problem, it is helpful to realize that all of these fractions are approximately equal to 3. If we sub1 1 tract 3 from each of the fractions, we get , , 134 26 3 1 2 , , and , respectively. Clearly, the great34 176 73 1 est of these is and is therefore the greatest of the 26 five given fractions. Another method of solving this type of numerical comparison problem is to convert the fractions to decimals by dividing the numerator by the denominator. (127, 128)

7.

Choice C is correct. This is another business problem, this time asking for percentage profit. Let the original price be P. Then the marked-up price will be 1.4(P). Ten percent is taken off this price, to yield a final price of (0.90) (1.40) (P), or (1.26) (P). Thus, the fractional increase was 0.26, so the percent increase was 26%. (118)

8.

Choice A is correct. Remember that the phrase “percent of” may be replaced by a multiplication sign. Thus, 0.05 % 6.5 0.0005 6.5, so the answer is 0.00325. (114)

9.

Choice C is correct. First, add the fractions in the 1 1 1 numerator to obtain 13 . Then divide 13 by 4 . 2 2 2 If you cannot see immediately that the answer is 3, you can convert the halves to decimals and divide, or you can express the fractions in terms of their 1 27 1 9 common denominator, thus: 13 ; 4 ; 2 2 2 2 27 9 27 2 54 3. (110, 112) 2 2 2 9 18

10. Choice C is correct. This is a proportion problem. If

x is the number of men needed to chop down 20 trees, then we form the proportion: 8 men : 28 trees 20 8 20 men : x trees, or . Solving for x, we x 28 (28)(20) (120) get x , or x 70. 8 15 7 3 3 15 7 100 49 9 100 49 9 Canceling 7 out of the numerator and denominator

11. Choice B is correct. .

3 15 gives us . Canceling 5 out of the 100 7 9

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3 3 numerator and denominator gives us . 20 7 9 Finally, canceling 9 out of both numerator and 1 1 (111) denominator gives us , or . 20 7 140 12. Choice A is correct. Percent error (absolute

error) (correct measurement) 5 77 0.0649 (approximately) 100 6.49 %. (117)

13. Choice C is correct. Profit on each dozen pens

selling price cost 12(25¢) $2.50 $3.00 $2.50 50¢, profit per dozen. Total profit profit per dozen number of dozens 50¢ 1440 $720.00. (118)

14. Choice B is correct. If 1 inch represents 1,000

miles, then 1 square inch represents 1,000 miles squared, or 1,000,000 square miles. Thus, the area would be represented by 16 squares of this size, or 16 square inches. (120) 15. Choice C is correct. Let V equal the new volume.

h Then if r 2r is the new radius, and h is the 3 1 1 4 2 2 h new height, V p(r ) (h ) p(2r) 3 3 3 9 4 2 pr h V, so the ratio V : V is equal to 4 : 3. (122) 3

16 192 47 235 10 200 1 192 , , and . Then, 5 60 12 60 3 60 3 60 235 200 1 627 209 . (101, 105, 109) 60 60 3 60 60

20. Choice E is correct. If it takes 16 faucets 10 hours

to fill 8 tubs, then it takes 1 faucet 160 hours to fill 8 tubs (16 faucets : 1 faucet x hours : 10 hours; x 16 ; x 160). If it takes 1 faucet 160 hours to 10 1 fill 8 tubs, then (dividing by 8) it takes 1 faucet 20 hours to fill 1 tub. If it takes 1 faucet 20 hours to fill 1 tub, then it takes 1 faucet 180 hours (9 20 hours) to fill 9 tubs. If it takes 1 faucet 180 hours 180 to fill 9 tubs, then it takes 12 faucets or 15 12 hours to fill 9 tubs. (120) 21. Choice E is correct. Let P be the original price.

Then 0.08P 96¢, so that 8P $96, or P $12. Adding the tax, which equals 96¢, we obtain our final price of $12.96. (118) 22. Choice B is correct. The number of girls who wear

glasses is 20 % of 40 % of the children in the class. Thus, the indicated operation is multiplication; 20 % 40 % 0.20 0.40 0.08 8 %. (114)

16. Choice A is correct. All of these fractions are

23. Choice B is correct. 1.2 % 0.5 0.012 0.5

1 1 approximately equal to . Thus, by subtracting 4 4 from each one we get remainders of, respectively,

24. Choice E is correct. Here, we can use as an

6.05 0.25 2 0.225 21.75 , , , , and . The 163 501 700 42.7 3715 first of these is the smallest. That is because of all of the negative fractions, it has the largest value without its sign. Therefore, it is the most negative 34.7 and, consequently, the smallest so that is the 163 desired answer.

(123–128)

17. Choice E is correct. Let N the original cost of

a radio. Then, original profit 45 % N. New profit 40 % 110 %N 44 % N. Thus, the ratio of new profit to original profit is 44 : 45. (118)

18. Choice A is correct.

1.3% 0.26 0.013 0.26 0.00338. 1 3

0.006.

(114)

3 4 approximate value for all the fractions. Subtracting

3 1.75 0.25 from each, we get remainders of: , , 4 369 179 1.00 2.00 1.00 , , and . Clearly, the last of 144 476 352 these is the greatest (it is the only positive one), so 256 is the fraction that is the largest. This problem 352 may also be solved by converting the fractions to decimals. (104, 123, 127) 25. Choice D is correct. Area length width. The

new area will be equal to the new length (2.20 times the old length) times the new width (0.80 times the old width), giving a product of 1.76 times the original area, an increase of 76 %. (122)

(114) 47 12

10 3

19. Choice D is correct. Average 3.2 .

320 16 The decimal 3.2 , and the lowest com100 5 mon denominator of the three fractions is 60, then

26. Choice B is correct. Total cost to merchant

$25.00 $15.00 $40.00. Profit selling price cost $50 $40 $10. Percent profit profit cost $10 $40 25 %. (118)

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188 • COMPLETE SAT MATH REFRESHER 27. Choice D is correct. We can convert the fractions

to decimals or to fractions with a lowest common denominator. Inspection will show that all sets of fractions contain the same members; therefore, if we convert one set to decimals or find the lowest common denominator for one set, we can use our results for all sets. Converting a fraction to a decimal involves only one operation, a single division, whereas converting to the lowest common denominator involves a multiplication, which must be followed by a division and a multiplication to change each fraction to one with the lowest common denominator. Thus, conversion to decimals is often 10 2 the simpler method: 0.769; 0.666; 13 3 3 5 7 0.636; 0.600; 0.555. (104) 5 9 11 However, in this case there is an even simpler method. Convert two of the fractions to equivalent 3 2 5 6 6 8 fractions: and . We now have , , 5 3 9 10 10 12 10 7 8 , , and . Remember this rule: When the 13 11 12 numerator and denominator of a fraction are both positive, adding 1 to both will bring the value of the 3 21 fraction closer to 1. (For example, , so 4 31 3 2 is closer to 1 than and is therefore the greater 4 3 5 6 fraction.) Thus we see that is less than , which 9 10 7 8 is less than , which is less than , which is less 11 12 10 10 9 9 than . is obviously less than , so must 13 13 13 13 be the greatest fraction. Thus, in decreasing order 10 2 7 3 5 the fractions are , , , , and . This method 13 3 11 5 9 is a great time-saver once you become accustomed to it. 28. Choice D is correct. The formula governing this

situation is C pd, where C circumference, and d diameter. Thus, if the new diameter is d 2d, then the new circumference is C pd 2pd 2C. Thus, the new, larger circle has a circumference of twice that of the original circle. (122) 29. Choice A is correct. The most important feature of

this problem is recognizing that the scale does not affect percent (or fractional) error, since it simply results in multiplying the numerator and denominator of a fraction by the same factor. Thus, we need only calculate the original percent error. Although it would not be incorrect to calculate the

full-scale percent error, it would be time-consuming and might result in unnecessary errors.) Absolute error 0.4. Actual measurement 6.0. Therefore, percent error (absolute error actual 0.4 measurement) 100% 100%, which equals 6.0 6.7% (approximately). (117) 30. Choice E is correct. Total cost number of sets

cost of each 24 $300 $7200. Revenue (number sold at 25% profit price at 25% profit) (number sold at 30% loss

price at 30% loss) (16 $375) (8 $210) $6000 $1680 $7680. Profit revenue cost $7680 $7200 $480. (118) 1 2

1 3 123 41 15 8 . 120 40 120 120

1 8

1 15

60 120

40 120

31. Choice C is correct.

2 3

(110) 2 300

180 300

32. Choice C is correct. % 90 90

6 0.6. 10

(114)

33. Choice D is correct. If the man makes 12 payments

of $31.50, he pays back a total of $378.00. Since the loan is for $360.00, his net interest is $18.00. There$18.00 fore, his rate of interest is , which can be $360.00 reduced to 0.05, or 5%.

(118)

34. Choice C is correct. Final selling price 85 %

1 130 % cost 110 cost. Thus, $86.19 2 1.105C, where C cost. C $86.19 1.105 $78.00 (exactly). (118) 35. Choice C is correct. If x is the amount of flour

needed for 8 people, then we can set up the propor1 tion 2 cups : 6 people x : 8 people. Solving for x 4 8 1 8 9 (120) gives us x 2 or 3. 6 4 6 4 36. Choice D is correct. If 10 men can survive for 24

days on 15 cans, then 1 man can survive for 240 days on 15 cans. If 1 man can survive for 240 days 240 on 15 cans, then 1 man can survive for or 16 15 days on 1 can. If 1 man can survive for 16 days on 1 16 can, then 8 men can survive for or 2 days on 1 8

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can. If 8 men can survive for 2 days on 1 can, then 36 for 36 days 8 men need or 18 cans to survive. 2 (120) 1 15

4 5

37. Choice D is correct. 1 feet 12 inches. Thus,

1 we have the proportion: inch : 1 mile 12.8 2 inches : x. Solving for x, we have x 25.6 miles 3 (120) 25 miles. 5 e f

38. Choice D is correct. If e hf, then h . If e

is doubled and f is halved, then the new value 2e 1 f . Multiplying the numerator of h, h 2 4e and denominator by 2 gives us h . Since f e 4e h and h we see that h 4h. This is f f

the same as saying that h is multiplied by 4. (122) 39. Choice E is correct. 3 inches : 2 yards 3 inches :

72 inches 3 : 72.

(121)

40. Choice D is correct. If Carl and Mark work for the

same length of time, then Carl will earn $8.00 for every $6.00 Mark earns (since in the time Mark can earn one $6.00 wage, Carl can earn two $4.00 wages). Thus, their hourly wage rates are in the ratio $6.00 (Mark) : $8.00 (Carl) 3 : 4. (120) 41. Choice D is correct. The lowest common denomi-

nator is the smallest number that is divisible by all of the denominators. Thus we are looking for the smallest number that is divisible by 6, 27, 5, 10, and 15. The smallest number that is divisible by 6 and 27 is 54. The smallest number that is divisible by 54 and 5 is 270. Since 270 is divisible by 10 and 15 also, it is the lowest common denominator. (110, 126) 42. Choice E is correct.

absolute deviation Percent deviation average score 100%. Absolute deviation Ralph’s score average score 90 85 5. 5 Percent deviation 100 % 500 % 85 85 5.88% (approximately). 5.88% is closer to 5.9% than to 5.8%, so 5.9% is correct. (117)

43. Choice B is correct. If we discount 20% and then

12%, we are, in effect, taking 88% of 80% of the original price. Since “of ” represents multiplication, when we deal with percent we can multiply 88% 80% 70.4%. This is a deduction of 29.6% from the original price. (119, 114) 44. Choice A is correct.

1 inch 1 foot 2 This is a simple proportion: 1 mile . Our x 2 first step must be to convert all these measurements to one unit. The most logical unit is the one 1 ft. 24 1 ft. our answer will take—feet. Thus, x . 2,640 ft. (1 mile equals 5,280 feet.) Solving for x, we find 2,640 x feet 110 feet. (120, 121) 24

45. Choice A is correct. Let the two original sides of

the rectangle be a and b, and the new sides be a 5a and b . We know that a 1.25a , and that 4 5a(b ) 4 ab (a )(b ) . Therefore, b b, a 4 5 1 (122) decrease of , or 20%. 5

46. Choice C is correct. The first thing to notice is that

these fractions are all approximately equal to 3. Thus, it will aid our comparison if we subtract 3 from each of the numbers and compare the remain170 99 ders instead. The five remainders are: , , 2,071 1,463 209 46 123 , , and , respectively. We must 1,772 2,963 2,631 find the smallest of these remainders, which is obviously the third one (the fourth and fifth are 1 positive, and the other two are greater than ). 10 5,107 Thus, the third choice, , is the smallest one. 1,772 (123–128) 47. Choice D is correct. Let’s say that the price was

$100 during 2003. 30% of $100 $30 so the new price in 2003 was $130. In 2004, the company cut back its prices 20% so the new price in 2004 $130 (20/100)$130 $130 (1/5)$130 $130 $26 $104. The net change is $104 $100 $4. $4/$100 4% increase (118)

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0.04 100

4 10,000

48. Choice E is correct. 0.04 %

1 . 2,500

(107)

49. Choice D is correct. Before adding you should

examine the numbers to be added. They form pairs, like this: 16 (12 88) (34 66) (21 79) (11 89), which equals 16 100 100 100 16 100 416. Dividing 416 by 25, we obtain 16, 25 which equals 16.64.

(112)

50. Choice A is correct. We can set up a proportion as

follows: 1 coconut 2 1 banana 1 , , so by multiplying 1 banana 1 1 grapefruit 3 the two equations together and and 1 banana 1 3 1 grapefruit 1 coconut

1 banana

2

1

canceling the bananas and the 1’s in the numerators 2 1 cocon ut and denominators, we get: . 3 1 grapefr uit (120)

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MATH REFRESHER SESSION 2

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Rate Problems: Distance and Time, Work, Mixture, and Cost

Word Problem Setup 200. Some problems require translation of words into algebraic expressions or equations. For example: 8 more than 7 times a number is 22. Find the number. Let n the number. We have 7n 8 22

7n 14

n2

Another example: There are 3 times as many boys as girls in a class. What is the ratio of boys to the total number of students? Let n number of girls. Then 3n number of boys 4n Total number of students n umber of boys 3n 3 T otal s tudents 4n 4 201. Rate problems concern a special type of relationship that is very common: rate input output. This results from the definition of rate as the ratio between output and input. In these problems, input may represent any type of “investment,” but the most frequent quantities used as inputs are time, work, and money. Output is usually distance traveled, work done, or money spent. Note that the word per, as used in rates, signifies a ratio. Thus a rate of 25 miles per hour signifies the ratio between an output of 25 miles and an input of 1 hour. 25 miles Frequently, the word per will be represented by the fraction sign, thus . 1 hour Example: Peter can walk a mile in 10 minutes. He can travel a mile on his bicycle in 2 minutes. How far away is his uncle’s house if Peter can walk there and bicycle back in 1 hour exactly? To solve a rate problem such as the one above, follow these steps: STEP 1. Determine the names of the quantities that represent input, output, and rate in the problem you are doing. In the example, Peter’s input is time, and his output is distance. His rate will be distance per unit of time, which is commonly called speed. STEP 2. Write down the fundamental relationship in terms of the quantities mentioned, making each the heading of a column. In the example, set up the table like this: speed time distance STEP 3. Directly below the name of each quantity, write the unit of measurement in terms of the answer you want. Your choice of unit should be the most convenient one, but remember, once you have chosen a unit, you must convert all quantities to that unit. We must select a unit of time. Since a minute was the unit used in the problem, it is the most logical choice. Similarly, we will choose a mile for our unit of distance. Speed (which is the ratio of

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distance to time) will therefore be expressed in miles per minute, usually abbreviated as mi/min. Thus, our chart now looks like this:

STEP 4. The problem will mention various situations in which some quantity of input is used to get a certain quantity of output. Represent each of these situations on a different line of the table, leaving blanks for unknown quantities. In the sample problem, four situations are mentioned: Peter can walk a mile in 10 minutes; he can bicycle a mile in 2 minutes; he walks to his uncle’s house; and he bicycles home. On the diagram , with the appropriate boxes filled, the problem will look like this:

STEP 5. From the chart and from the relationship at the top of the chart, quantities for filling some of the empty spaces may become obvious. Fill in these values directly. In the example, on the first line of the chart, we see that the walking speed times 10 equals 1. 1 mi Thus, the walking speed is 0.1 mi/min (mi/min 10 1 mi; mi/min 0.1). 10 min Similarly, on the second we see that the bicycle speed equals 0.5 mi/min. Furthermore, his walking speed shown on line 3 will be 0.1, the same speed as on line 1; and his bicycling speed shown on line 4 will equal the speed (0.5) shown on line 2. Adding this information to our table, we get:

STEP 6. Next, fill in the blanks with algebraic expressions to represent the quantities indicated, being careful to take advantage of simple relationships stated in the problem or appearing in the chart. Continuing the example, we represent the time spent traveling shown on line 3 by x. According to the fundamental relationship, the distance traveled on this trip must be (0.1) x. Similarly, if y represents the time shown on line 4, the distance traveled is (0.5) y. Thus our chart now looks like this:

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STEP 7. Now, from the statement of the problem, you should be able to set up enough equations to solve for all the unknowns. In the example, there are two facts that we have not used yet. First, since Peter is going to his uncle’s house and back, it is assumed that the distances covered on the two trips are equal. Thus we get the equation: (0.1) x (0.5) y. We are told that the total time to and from his uncle’s house is one hour. Since we are using minutes as our unit of time, we convert the one hour to 60 minutes. Thus we get the equation: x y 60. Solving these two equations (0.l x 0.5y and x y 60) algebraically, we find that x 50 and y 10. (See Section 407 for the solution of simultaneous equations.) STEP 8. Now that you have all the information necessary, you can calculate the answer required. In the sample problem we are required to determine the distance to the uncle’s house, which is (0.1) x or (0.5) y. Using x 50 or y 10 gives us the distance as 5 miles. Now that we have shown the fundamental steps in solving a rate problem, we shall discuss various types of rate problems.

Distance and Time 202. In distance and time problems the fundamental relationship that we use is speed time distance. Speed is the rate, time is the input, and distance is the output. The example in Section 201 was this type of problem. Example: In a sports car race, David gives Kenny a head start of 10 miles. David’s car goes 80 miles per hour and Kenny’s car goes 60 miles per hour. How long should it take David to catch up to Kenny if they both leave their starting marks at the same time? STEP 1. Here the fundamental quantities are speed, time, and distance. STEP 2. The fundamental relationship is speed time distance. Write this at the top of the chart. STEP 3. The unit for distance in this problem will be a mile. The unit for speed will be miles per hour. Since the speed is in miles per hour, our time will be in hours. Now our chart looks like this:

STEP 4. The problem offers us certain information that we can add to the chart. First we must make two horizontal rows, one for Kenny and one for David. We know that Kenny’s speed is 60 miles per hour and that David’s speed is 80 miles per hour. STEP 5. In this case, none of the information in the chart can be used to calculate other information in the chart. STEP 6. Now we must use algebraic expressions to represent the unknowns. We know that

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both Kenny and David travel for the same amount of time, but we do not know for how much time, so we will place an x in the space for each boy’s time. Now from the relationship of speed

time distance, we can calculate Kenny’s distance as 60x and David’s distance as 80x. Now the chart looks like this:

STEP 7. From the statement of the problem we know that David gave Kenny a 10-mile head start. In other words, David’s distance is 10 more miles than Kenny’s distance. This can be stated algebraically as 60x 10 80x. That is, Kenny’s distance 10 miles David’s distance. 1 Solving for x gives us x . 2 STEP 8.

The question asks how much time is required for David to catch up to Kenny. If we

1 look at the chart, we see that this time is x, and x has already been calculated as so the 2 1 answer is hour. 2

Work 203. In work problems the input is time and output is the amount of work done. The rate is the work per unit of time. 1 Example: Jack can chop down 20 trees in 1 hour, whereas it takes Ted 1 hours to chop 2 down 18 trees. If the two of them work together, how long will it take them to chop down 48 trees? Solution: By the end of Step 5 your chart should look like this:

In Step 6, we represent the time that it takes Jack by x in line 3. Since we have the relationship that rate time work, we see that in line 3 the work is 20x. Since the two boys work together (therefore, for the same amount of time), the time in line 4 must be x, and the work must be 12x. Now, in Step 7, we see that the total work is 48 trees. From lines 3 and 1 4, then, 20x 12x 48. Solving for x gives us x 1. We are asked to find the number of 2

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hours needed by the boys to chop down the 48 trees together, and we see that this time is 1 x, or 1 hours. 2

Mixture 204. In mixture problems you are given a percent or a fractional composition of a substance, and you are asked questions about the weights and compositions of the substances. The basic relationship here is that the percentage of a certain substance in a mixture the amount of the mixture the amount of substance. Note that it is often better to change percents to decimals because it makes it easier to avoid errors. Example: A chemist has two quarts of 25% acid solution and one quart of 40% acid solution. If he mixes these, what will be the concentration of the mixture? Solution: Let x concentration of the mixture. At the end of Step 6, our table will look like this:

We now have one additional bit of information: The amount of acid in the mixture must be equal to the total amount of acid in each of the two parts, so 3x 0.50 0.40. Therefore x is equal to 0.30, which is the same as a 30% concentration of the acid in the mixture.

Cost 205. In cost problems the rate is the price per item, the input is the number of items, and the output is the value of the items considered. When you are dealing with dollars and cents, you must be very careful to use the decimal point correctly. Example: Jim has $3.00 in nickels and dimes in his pocket. If he has twice as many nickels as he has dimes, how many coins does he have altogether? Solution: After Step 6, our chart should look like this (where c is the number of dimes Jim has):

Now we recall the additional bit of information that the total value of the nickels and dimes is $3.00, or 300 cents. Thus, 5(2c) 10c 300; 20c 300; so c 15, the number of dimes. Jim has twice as many nickels, so 2c 30.

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The total number of coins is c 2c 3c 45. The following table will serve as review for this Refresher Section.

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Practice Test 2 Rate Problems: Distance and Time, Work, Mixture, and Cost Correct answers and solutions follow each test. 1.

A

B

C

D

E

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1. A man rowed 3 miles upstream in 90 minutes. If the river flowed with a current of 2 miles

per hour, how long did the man’s return trip take? (A) (B) (C) (D) (E)

2.

3.

A

B

C

D

E

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A

B

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D

E

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2. Charles can do a job in 1 hour, Bill can do the same job in 2 hours, and Bob can do the job

in 3 hours. How long does it take them to do the job working together? 6 (A) hours 11 1 (B) hour 2 (C) 6 hours 1 (D) hours 3 1 (E) hours 6 3. Mr. Smith had $2,000 to invest. He invested part of it at 5% per year and the remainder at

4% per year. After one year, his investment grew to $2,095. How much of the original investment was at the 5% rate? (A) $500 (B) $750 (C) $1,000 (D) $1,250 (E) $1,500

4.

A

B

C

D

E

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4. A man walks down the road for half an hour at an average speed of 3 miles per hour.

He waits 10 minutes for a bus, which brings him back to his starting point at 3:15. If the man began his walk at 2:25 the same afternoon, what was the average speed of the bus? (A) (B) (C) (D) (E)

5.

A

B

C

D

E

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1.5 miles per hour 3 miles per hour 4.5 miles per hour 6 miles per hour 9 miles per hour

5. Faucet A lets water flow into a 5-gallon tub at a rate of 1.5 gallons per minute. Faucet B

lets water flow into the same tub at a rate of 1.0 gallons per minute. Faucet A runs alone for 100 seconds; then the two of them together finish filling up the tub. How long does the whole operation take? (A) (B) (C) (D) (E)

120 seconds 150 seconds 160 seconds 180 seconds 190 seconds

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6.

A

B

C

D

E

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6. Coffee A normally costs 75¢ per pound. It is mixed with Coffee B, which normally

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costs 80¢ per pound, to form a mixture that costs 78¢ per pound. If there are 10 pounds of the mix, how many pounds of Coffee A were used in the mix? (A) (B) (C) (D) (E)

7.

A

B

C

D

E

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3 4 4.5 5 6

7. If a man can run p miles in x minutes, how long will it take him to run q miles at the same

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rate? pq (A) x minutes px (B) q minutes q (C) minutes px qx (D) minutes p x (E) minutes pq

8.

A

B

C

D

E

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8. A train went 300 miles from City X to City Y at an average rate of 80 mph. At what

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speed did it travel on the way back if its average speed for the whole trip was 100 mph? (A) 120 mph (B) 125 mph 1 (C) 133 mph 3 1 (D) 137 mph 2 (E) 150 mph

9.

10.

A

B

C

D

E

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9. A man spent exactly $2.50 on 3¢, 6¢, and 10¢ stamps. If he bought ten 3¢ stamps and

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twice as many 6¢ stamps as 10¢ stamps, how many 10¢ stamps did he buy? (A) 5 (B) 10 (C) 12 (D) 15 (E) 20

A

B

C

D

E

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10. If 6 workers can complete 9 identical jobs in 3 days, how long will it take 4 workers to

complete 10 such jobs? (A) (B) (C) (D) (E)

3 days 4 days 5 days 6 days more than 6 days

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11.

A

B

C

D

E

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11. A barge travels twice as fast when it is empty as when it is full. If it travels 20 miles north

with a cargo, spends 20 minutes unloading, and returns to its original port empty, taking 8 hours to complete the entire trip, what is the speed of the barge when it is empty? (A) (B) (C) (D) (E)

12.

A

B

C

D

E

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12. Bill can hammer 20 nails in 6 minutes. Jeff can do the same job in only 5 minutes. How

long will it take them to finish if Bill hammers the first 5 nails, then Jeff hammers for 3 minutes, then Bill finishes the job? (A) (B) (C) (D) (E)

13.

A

B

C

D

E

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A

B

C

D

E

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them, what will be the concentration (to the nearest percent) of the resulting solution?

A

B

C

D

E

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the following cannot be the number of quarters he has?

A

B

C

D

E

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1 2 3 4 5

15. Jim’s allowance is $1.20 per week. Stan’s is 25¢ per day. How long will they have to

save, if they save both their allowances together, before they can get a model car set that costs $23.60? (A) (B) (C) (D) (E)

16.

22% 23 % 24 % 25 % 26 %

14. Robert has 12 coins totaling $1.45. None of his coins is larger than a quarter. Which of

(A) (B) (C) (D) (E) 15.

4.6 minutes 5.0 minutes 5.4 minutes 5.8 minutes 6.0 minutes

13. Jack has two quarts of a 30% acid solution and three pints of a 20% solution. If he mixes

(A) (B) (C) (D) (E) 14.

less than 3 mph less than 4 mph but not less than 3 mph less than 6 mph but not less than 4 mph less than 8 mph but not less than 6 mph 8 mph or more

6 weeks 8 weeks 10 weeks 13 weeks 16 weeks

16. Chuck can earn money at the following schedule: $2.00 for the first hour, $2.50 an hour

for the next two hours, and $3.00 an hour after that. He also has the opportunity of taking a different job that pays $2.75 an hour. He wants to work until he has earned $15.00. Which of the following is true? (A) (B) (C) (D) (E)

The first job will take him longer by 15 minutes or more. The first job will take him longer by less than 15 minutes. The two jobs will take the same length of time. The second job will take him longer by 30 minutes or more. The second job will take him longer by less than 10 minutes.

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17.

A

B

C

D

E

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17. If Robert can seal 40 envelopes in one minute, and Paul can do the same job in 80

seconds, how many minutes (to the nearest minute) will it take the two of them, working together, to seal 350 envelopes? (A) (B) (C) (D) (E)

18.

A

B

C

D

E

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18. Towns A and B are 400 miles apart. If a train leaves A in the direction of B at 50 miles

per hour, how long will it take before that train meets another train, going from B to A, at a speed of 30 miles per hour? (A) 4 hours 1 (B) 4 hours 3 (C) 5 hours 2 (D) 5 hours 3 2 (E) 6 hours 3

19.

A

B

C

D

E

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19. A tub is shaped like a rectangular solid, with internal measurements of 2 feet 2 feet 5

feet. If two faucets, each with an output of 2 cubic feet of water per minute, pour water into the tub simultaneously, how many minutes does it take to fill the tub completely? (A) (B) (C) (D) (E)

20.

A

B

C

D

E

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20. A 30 % solution of barium chloride is mixed with 10 grams of water to form a 20 %

solution. How many grams of the original solution did we start with? (A) (B) (C) (D) (E)

21.

A

B

C

D

E

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less than 3 minutes less than 4 minutes, but not less than 3 less than 5 minutes, but not less than 4 less than 6 minutes, but not less than 5 6 minutes or more

10 15 20 25 30

21. Mr. Adams had a coin collection including only nickels, dimes, and quarters. He had

twice as many dimes as he had nickels, and half as many quarters as he had nickels. If the total face value of his collection was $300.00, how many quarters did the collection contain? (A) (B) (C) (D) (E)

75 100 250 400 800

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22.

A

B

C

D

E

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22. A storekeeper stocks a high-priced pen and a lower-priced model. If he sells the high-

priced pens, which yield a profit of $1.20 per pen sold, he can sell 30 in a month. If he sells the lower-priced pens, making a profit of 15¢ per pen sold, he can sell 250 pens in a month. Which type of pen will yield more profit per month, and by how much? (A) (B) (C) (D) (E)

23.

A

B

C

D

E

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23. At a cost of $2.50 per square yard, what would be the price of carpeting a rectangular

floor, 18 24 ? (A) (B) (C) (D) (E)

24.

A

B

C

D

E

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The cheaper pen will yield a greater profit, by $1.50. The more expensive pen will yield a greater profit, by $1.50. The cheaper pen will yield a greater profit, by 15¢. The more expensive pen will yield a greater profit, by 15¢. Both pens will yield exactly the same profit.

$120 $360 $750 $1,000 $1,080

24. Tom and Bill agreed to race across a 50-foot pool and back again. They started together,

but Tom finished 10 feet ahead of Bill. If their rates were constant, and Tom finished the race in 27 seconds, how long did Bill take to finish it? (A) 28 seconds (B) 30 seconds 1 (C) 33 seconds 3 (D) 35 seconds (E) 37 seconds

25.

A

B

C

D

E

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25. If four men need $24.00 worth of food for a three-day camping trip, how much will two

men need for a two-week trip? (A) (B) (C) (D) (E)

26.

A

B

C

D

E

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$12.00 $24.00 $28.00 $42.00 $56.00

26. A man walks 15 blocks to work every morning at a rate of 2 miles per hour. If there are

20 blocks in a mile, how long does it take him to walk to work? 1 (A) 12 minutes 2 (B) 15 minutes 1 (C) 22 minutes 2 1 (D) 37 minutes 2 (E) 45 minutes

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27.

A

B

C

D

E

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27. A certain river has a current of 3 miles per hour. A boat takes twice as long to travel

upstream between two points as it does to travel downstream between the same two points. What is the speed of the boat in still water? (A) (B) (C) (D) (E)

28.

A

B

C

D

E

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28. Stan can run 10 miles per hour, whereas Jack can run only 8 miles per hour. If they start

at the same time from the same point and run in opposite directions, how far apart (to the nearest mile) will they be after 10 minutes? (A) (B) (C) (D) (E)

29.

A

B

C

D

E

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3 miles per hour 6 miles per hour 9 miles per hour 12 miles per hour The speed cannot be determined from the given information.

1 mile 2 miles 3 miles 4 miles 5 miles

29. Machine A can produce 40 bolts per minute, whereas Machine B can produce only 30

1 per minute. Machine A begins alone to make bolts, but it breaks down after 1 minutes, 2 and Machine B must complete the job. If the job requires 300 bolts, how long does the whole operation take? 1 (A) 7 minutes 2 (B) 8 minutes 1 (C) 8 minutes 2 (D) 9 minutes 1 (E) 9 minutes 2

30.

A

B

C

D

E

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30. Ten pints of 15 % salt solution are mixed with 15 pints of 10 % salt solution. What is the

concentration of the resulting solution? (A) (B) (C) (D) (E)

31.

A

B

C

D

E

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10 % 12 % 12.5 % 13 % 15 %

31. Jeff makes $5.00 every day, from which he must spend $3.00 for various expenses. Pete

makes $10.00 a day but has to spend $7.00 each day for expenses. If the two of them save together, how long will it take before they can buy a $150 car? (A) (B) (C) (D) (E)

10 days 15 days 30 days 50 days 75 days

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32.

A

B

C

D

E

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32. Two cities are 800 miles apart. At 3:00 P.M., Plane A leaves one city, traveling toward the

other city at a speed of 600 miles per hour. At 4:00 the same afternoon, Plane B leaves the first city, traveling in the same direction at a rate of 800 miles per hour. Which of the following answers represents the actual result? (A) (B) (C) (D) (E)

33.

A

B

C

D

E

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33. Peter has as many nickels as Charlie has dimes; Charlie has twice as many nickels as

Peter has dimes. If together they have $2.50 in nickels and dimes, how many nickels does Peter have? (A) (B) (C) (D) (E)

34.

A

B

C

D

E

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A

B

C

D

E

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miles per hour, or he can travel halfway at 50 miles per hour, then slow down to 30 miles per hour for the second 60 miles. Which way is faster, and by how much?

A

B

C

D

E

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The constant rate is faster by 10 minutes or more. The constant rate is faster by less than 10 minutes. The two ways take exactly the same time. The constant rate is slower by less than 10 minutes. The constant rate is slower by 10 minutes or more.

35. John walks 10 miles at an average rate of 2 miles per hour and returns on a bicycle at an

average rate of 10 miles per hour. How long (to the nearest hour) does the entire trip take him? (A) (B) (C) (D) (E)

36.

1 nickel 4 nickels 7 nickels 10 nickels The answer cannot be determined from the given information.

34. A man can travel 120 miles in either of two ways. He can travel at a constant rate of 40

(A) (B) (C) (D) (E) 35.

Plane A arrives first, by an hour or more. Plane A arrives first, by less than an hour. The two planes arrive at exactly the same time. Plane A arrives after Plane B, by less than an hour. Plane A arrives after Plane B, by an hour or more.

3 hours 4 hours 5 hours 6 hours 7 hours

36. If a plane can travel P miles in Q hours, how long will it take to travel R miles?

PQ (A) hours R P (B) hours QR QR (C) hours P Q (D) hours PR PR (E) hours Q

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37.

38.

A

B

C

D

E

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A

B

C

D

E

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37. A boy can swim 75 feet in 12 seconds. What is his rate to the nearest mile per hour?

(A) (B) (C) (D) (E)

38. How many pounds of a $1.20-per-pound nut mixture must be mixed with two pounds of

a 90¢-per-pound mixture to produce a mixture that sells for $1.00 per pound? (A) (B) (C) (D) (E)

39.

A

B

C

D

E

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A

B

C

D

E

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0.5 1.0 1.5 2.0 2.5

39. A broken clock is set correctly at 12:00 noon. However, it registers only 20 minutes for

each hour. In how many hours will it again register the correct time? (A) (B) (C) (D) (E)

40.

1 mph 2 mph 3 mph 4 mph 5 mph

12 18 24 30 36

40. If a man travels p hours at an average rate of q miles per hour, and then r hours at an

average rate of s miles per hour, what is his overall average rate of speed? pq rs (A) pr qs (B) 2 qs (C) pr p r (D) q s p r (E) s q

41.

A

B

C

D

E

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41. If Walt can paint 25 feet of fence in an hour, and Joe can paint 35 feet in an hour, how

many minutes will it take them to paint a 150-foot fence, if they work together? (A) (B) (C) (D) (E)

42.

A

B

C

D

E

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150 200 240 480 500

42. If a man travels for a half hour at a rate of 20 miles per hour, and for another half hour at

a rate of 30 miles per hour, what is his average speed? (A) (B) (C) (D) (E)

24 miles per hour 25 miles per hour 26 miles per hour 26.5 miles per hour The answer cannot be determined from the given information.

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43.

A

B

C

D

E

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43. New York is 3,000 miles from Los Angeles. Sol leaves New York aboard a plane heading

toward Los Angeles at the same time that Robert leaves Los Angeles aboard a plane heading toward New York. If Sol is moving at 200 miles per hour and Robert is moving at 400 miles per hour, how soon will one plane pass the other? (A) 2 hours 1 (B) 22 hours 2 (C) 5 hours (D) 4 hours (E) 12 hours

44.

A

B

C

D

E

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44. A man exchanged a dollar bill for change and received 7 coins, none of which were half

dollars. How many of these coins were dimes? (A) (B) (C) (D) (E)

45.

A

B

C

D

E

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45. A man adds two quarts of pure alcohol to a 30 % solution of alcohol in water. If the new

concentration is 40 %, how many quarts of the original solution were there? (A) (B) (C) (D) (E)

46.

A

B

C

D

E

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48.

A

B

C

D

E

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A

B

C

D

E

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12 15 18 20 24

46. A certain power company charges 8¢ per kilowatt-hour for the first 1000 kilowatt-hours,

and 6¢ per kilowatt-hour after that. If a man uses a 900-watt toaster for 5 hours, a 100-watt lamp for 25 hours, and a 5-watt clock for 400 hours, how much is he charged for the power he uses? (1 kilowatt 1,000 watts) (A) (B) (C) (D) (E)

47.

0 1 4 5 The answer cannot be determined from the information given.

56¢ 64¢ 72¢ $560.00 $720.00

47. At 30¢ per yard, what is the price of 96 inches of ribbon?

(A) (B) (C) (D) (E)

72¢ 75¢ 80¢ 84¢ 90¢ 1 2

48. A man travels for 6 hours at a rate of 50 miles per hour. His return trip takes him 7

hours. What is his average speed for the whole trip? (A) (B) (C) (D) (E)

44.4 miles per hour 45.0 miles per hour 46.8 miles per hour 48.2 miles per hour 50.0 miles per hour

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49.

A

B

C

D

E

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49. Stanley puts $100 in the bank for two years at 5 % interest compounded annually. At

the end of the two years, what is his balance? (A) (B) (C) (D) (E)

50.

A

B

C

D

E

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$100.00 $105.00 $105.25 $110.00 $110.25

50. A 12-gallon tub has a faucet that lets water in at a rate of 3 gallons per minute, and a drain

that lets water out at a rate of 1.5 gallons per minute. If you start with 3 gallons of water in the tub, how long will it take to fill the tub completely? (A) (B) (C) (D) (E)

3 minutes 4 minutes 6 minutes 7.5 minutes 8 minutes

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Now the speed of the boat downstream (with the current) is s 2, or 6 miles per hour. This is equal 3 3 1 to , and we get the equation 6, so t t t 2 hour. We must be careful with our units because the 1 answer must be in minutes. We can convert hour 2 to 30 minutes to get the final answer. (201, 202)


B A E E C B D C B C D C E

14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.

A B B B C D C D A A B E C

27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38.

C C E B C B E A D C D B

39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.

B A A B C E A C C A E C

2. Choice A is correct.

Answers and Solutions for Practice Test 2 1. Choice B is correct. The fundamental relationship

here is: rate time distance. The easiest units to work with are miles per hour for the rate, hours for time, and miles for distance. Note that the word per indicates division because when calculating a rate, we divide the number of miles (distance units) by the number of hours (time units).

Let r rate together and t time together. 1 1 11 Now, r 1 because whenever two or 2 3 6 more people are working together, their joint rate is the sum of their individual rates. This is not necessa rily true of the time or the work done. In this case, 11 6 we know that r t 1 and r , so t . 6 11

We can set up our chart with the information given. 1 We know that the upstream trip took 1 hours (90 2 minutes) and that the distance was 3 miles. Thus the upstream rate was 2 miles per hour. The downstream distance was also 3 miles, but we use t for the time, which is unknown. Thus the downstream

(201, 203) 3.


3 rate was . Our chart looks like this: t

We use the rest of the information to solve for t. We know that the speed of the current is 2 miles per hour. We assume the boat to be in still water and assign it a speed, s; then the upstream (against the current) speed of the boat is s 2 miles per hour. Since s 2 2, s 4.

Let x part of the $2,000 invested at 5 %. Let y part of $2,000 invested at 4 %. We know that since the whole $2,000 was invested, x y must equal $2,000. Furthermore, we know that the sum of the interests on both investments equaled $95, so 0.05x 0.04x 95. Since we have to solve only for x, we can express this as 0.01x 0.04x 0.04y 95. Then we factor out 0.04. Thus 0.01x 0.04 (x y) 95. Since we know that x y 2,000, we have 0.01x 0.04 (2,000) 95; 0.01x 80 95, and x 1,500. Thus, $1,500 was invested at 5 %. (201, 205)

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COMPLETE SAT MATH REFRESHER • 209 4. Choice E is correct.

Let a distance the man walks. Since the man 3 mi walks at 3 miles per hour, he walks at 60 min or 1 mi 1 mi 20 min . From this we can find a 20 min

1 30 min 1 miles. The total time he spent was 2 50 minutes (the difference between 3:15 and 2:25), and 30 10 t 50, so t must be equal to 10 minutes. This reduces our problem to the 1 simple equation 10r 1 (where r rate of the 2 bus), and, on solving, r 0.15 miles per minute. But the required answer is in miles per hour. In one hour, or 60 minutes, the bus can travel 60 times as far as the 0.15 miles it travels in one minute, so that the bus travels 60 0.15 9 miles per hour. (201, 202)

6. Choice B is correct.

Let x weight of Coffee A in the mix. Let y weight of Coffee B in the mix. We know that the weight of the mix is equal to the sum of the weights of its components. Thus, x y 10. Similarly, the cost of the mix is equal to the sum of the costs of the components. Thus, 75x 80y 780. Solving these two equations simultaneously gives us x 4 and y 6, so 4 pounds of Coffee A were used. (201, 204, 407) 7. Choice D is correct.


Let r rate of the man. Let t time it takes him to run q miles. From the first line, we know that rx p, then r p x. Substituting this in the second line, we get p qx x x t q, so t q p , or minutes. (201, 202) p

Let t time faucets A and B run together.


Let x amount of water delivered when A and B run together. We know that the total number of gallons is 5, and 5 A alone delivers 2.5 gallons (1.5 gal/min min 3 2.5 gal), so x equals 2.5. This leads us to the simple equation 2.5t 2.5, so t 1 minute, or 60 5 seconds. Thus, the whole operation takes t 3 minutes, or 100 60 seconds, totaling 160 seconds. (201, 203)

Let t time from city X to city Y. Let s time from city Y to city X.

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Let r rate of the train from Y to X.

11.


300 15 We know that 80t 300, so t , or . Also, 80 4 100(s t) 600, so s t 6. This and the last 15 equation lead us to the conclusion that s 6 , 4 9 or . Now, from the middle line, we have 4 9 400 1 r 300, so r , or 133 miles per hour. 4 3 3

(Note that the reason why we chose the equations in this particular order was that it is easiest to concentrate first on those with the most data already given.) (201, 202) 9.

Let r loaded rate; then


2r empty rate 20 1 10 Total time 8 hours. r 3 r Multiplying by 3r on both sides, we get 90 23r, so r 90 23, or about 3.9 miles per hour. However, the problem asks for the speed when empty, which is 2r, or 7.8. This is less than 8 mph, but not less than 6 mph. (201, 202) 12.


Let x the number of 10¢ stamps bought. We know that the total cost is 250¢, so 30 10x 1 2x 250. This is the same as 22x 220, so x 10. Therefore, he bought ten 10¢ stamps. (201, 205) 10. Choice C is correct.

Let r Bill’s rate. Let r rate of one worker.

Let s Jeff’s rate.

Let t time for 4 workers to do 10 jobs.

x number of nails left after Jeff takes his turn. 1 6r 20, so r 3. 3 5s 20, so s 4.

From the first line, we have 18r 9, so r 1/2. Substituting this in the second line, 4r 2, so 2t 10. Therefore t 5. The workers will take 5 days. (201, 203)

Total work 5 3s x 20 5 12 x, so x x 3. Thus 0.9. r 5 x Total time 3 1.5 3 0.9 5.4. r r (201, 203)

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13.


15.

(2 qts 4 pts)

(25¢/day $1.75/week)

Let x % concentration of new solution.

Let w the number of weeks they save.

4 pts of 30 % 3 pts of 20 % 7 pts of x %

Total money 295w 2,360.

1.2 pts 0.6 pt 1.8 pts

Therefore, w 2,360 295 8.

(x %) (7) 1.8, so x 180 7 25.7 (approximately), which is closest to 26 %. (201, 204) 14.



So, they must save for 8 weeks. 16.

(201, 205)


Let p number of pennies n number of nickels d number of dimes q number of quarters Total number of coins p n d q 12. Total value p 5n 10d 25q 145. Now, if q 1, then pnd 11, p5n 10d 120. But in this case, the greatest possible value of the other eleven coins would be the value of eleven dimes, or 110 cents, which falls short of the amount necessary to give a total of 145 cents for the twelve coins put together. Therefore, Robert cannot have only one quarter. (201, 205)

Let x hours at $3.00. Let y hours at $2.75. Total pay first job 200 500 300x 1,500, so 2 x 2. 3 2 2 Total time first job 1 2 2 5. 3 3 5 Total pay second job 275y 1500, so y 5. 11 5 Total time second job 5. 11 2 hour 40 minutes 3 2 5 hour 27.2727 . . . minutes (less than hour) 3 11 Thus, the first job will take him longer by less than 15 minutes.

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17.


20.


Let t time to seal 350 envelopes. Let x number of grams of original solution.

Paul’s rate is 30 envelopes/minute, as shown by the proportion:

Total weight and amounts of barium chloride may be added by column.

40 envelopes 30 envelopes rate 80 seconds 60 seconds

(20%) (10 x) 0.30x, so 10 x 1.50x, x 20. (201, 204)

Total work 70t 350, so t 5 minutes. (201, 203) 21. 18.



Let t time to meet. Total distance traveled by two trains together equals 50t 30t 80t 400 miles, so t 5 hrs. (201, 202) 19.

Let n number of nickels.

25n 1 Total value 5n 20n 37 n 2 2 30,000.


1 Thus, n 30,000 37 800. 2 n 800 The number of quarters is then 400. 2 2 (201, 205) 22.

Let t time to fill the tub.


Volume of tub 2 2 5 20 cu. ft. Rate 2 rate of each faucet 2 2 cu. ft./min. 4 cu. ft./min. Therefore, t 5 minutes.

(201, 203) Subtracting 3,600¢ from 3,750¢, we get 150¢. Thus, the cheaper pen yields a profit of 150¢, or $1.50, more per month than the more expensive one. (201, 205)

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23.


26.

Let t time to walk to work.

Area must be expressed in square yards; 18 6 yds, and 24 8 yds, so 18 24 6 yds 8 yds 48 sq yds. The cost would then be $2.50 48 $120.00. (201, 205) 24.

2 2 miles/hr 2 (20 blocks)/(60 min) 3 blocks/minute. 2 1 t 15 22 minutes. 3 2

Choice B is correct. 27.

Since the two trips cover the same distance, we can write the equation: h(r 3) 2h(r 3). Dividing by h, r 3 2r 6, so r 9. (201, 202)

Let t Bill’s time to finish the race.

28.

Choice C is correct. We could treat this as a regular distance problem and make up a table that would solve it, but there is an easier way here, if we consider the quantity representing the distance between the boys. This distance starts at zero and increases at the rate of 18 miles per hour. Thus, in 1 10 minutes, or hour, they will be 3 miles apart. 6 1 mi (201, 202) ( hr 18 3 mi). 6 hr

29.


Choice E is correct. This is a rate problem in which the fundamental relationship is rate time

number of men cost. The rate is in dollars/mandays. Thus, our chart looks like this:

The cost of the first trip is $24, so 12r 24 and r 2. The cost of the second trip is 28r, or $56. (201, 205)


Let r speed of the boat in still water.

Let s Bill’s rate.

25.

(201, 202)

Let h time to travel downstream.

Let r Tom’s rate.

100 27r 100, so r ; 27 90 10 27s 90, so s ; 27 3 10 10t st 100, and s , so 100, thus t 30. 3 3 (201, 202)


Let t time B works. Since A produces only 60 out of 300 that must be produced, B must produce 240; then, 30t 240, so t 8. 1 1 1 Total time t 1 8 1 9 . (201, 203) 2 2 2

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30.


1 hour, 20 minutes. Plane B: 800t 800, so t 1. Total time for plane A 1 hour, 20 minutes. Total time for plane B 1 hour 1 hour 2 hours. Thus, plane A arrives before plane B by 40 minutes (less than an hour). (201, 202) 33.


*One “pint” of salt actually represents a weight of salt equal to the weight of one pint of water.

Let x concentration of resulting solution. (x %) (25) 3.0, so x 300 25 12. 31.

(201, 204)


Let n number of Peter’s nickels. Let d number of Peter’s dimes. Total value of coins 5n 10d 10d 10n 15n 20d. Thus, 15n 20d 250. This has many different solutions, each of which is possible (e.g., n 2, d 11, or n 6, d 8, etc.). (201, 205)

(Net pay pay expenses.) Let d the number of days it takes to save. Total net pay $150.00, so 150 5d, thus d 30.

34.


Do not make the mistake of using 5 and 10 as the rates! (201, 205) 32.


Let h time to travel 120 miles at the constant rate. Let m time to travel 60 miles at 50 mi/hr. Let h time for trip at 600 mph waiting time before second flight. Let t time for trip at 800 mph. 800 1 Plane A: 600h 800, so h 1 hours 600 3

Let n time to travel 60 miles at 30 mi/hr. Forming the equations for h, m, and n, and solving, we get: 120 40h 120; h ; h 3 40 60 50m 60; m ; m 1.2 50

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60 30n 60; n ; n 2 30 Total time with constant rate h 3 hours.

1 75 75 feet 75(mile) mile 5,280 5,280 1 1 12 seconds 12( hour) hour 3,600 300

Total time with changing rate m n 3.2 hours.

22,500 75 1 4.3(approximately) r 5,280 5,280 300

Thus, the constant rate is faster by 0.2 hours, or 12 minutes. (201, 202) 35.


4 mi/hr (approximately). 38.

(201, 202)


Let h time to walk. Let t time to bicycle.

Let x pounds of $1.20 mixture.

Forming equations: 2h 10, so h 5; and 10t 10, so t 1.

Total value of mixture 100(x 2) 180 120x.

Total time h t 5 1 6. 36.


39.

Let t hours to register the correct time.

Let y time to travel R miles. P Qx P, so x . Q

P RQ xy y R, so y hours time to Q P

37.


Let r rate of swimming.


(Loss is the amount by which the clock time differ s from real time.)

Let x rate of traveling Q miles.

travel R miles.

100x 200 180 120x, so x 1 pound. (201, 204)

(201, 202)

(201, 202)

If the clock registers only 20 minutes each hour, it 2 loses 40 minutes, or hour each hour. The clock 3 will register the correct time only if it has lost some multiple of 12 hours. The first time this can 2 occur is after it has lost 12 hours. t 12, so 3 t 18 hours. (201)

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40.


43.


Let t time from simultaneous departure to meeting. Let x average speed.

Sol’s time is equal to Robert’s time because they leave at the same time and then they meet. Their combined distance is 3,000 miles, so 200t 400t 3,000, or t 5 hours. (201, 202)

We may add times of travel at the two rates, and also add the distances. Then, x( p r) pq rs; pq rs (201, 202) thus, x . pr 44. 41.

Let x the time the job takes. Since they are working together, we add their rates and the amount of work they do. Thus, 60x 150, so x 2.5 (hours) 150 minutes. (201, 203) 42.




Let p number of pennies. Let n number of nickels. Let d number of dimes. Let q number of quarters. Adding the numbers of coins and their values, we get p n d q 7, and p 5n 10d 25q 100. These equations are satisfied by several values of p, n, d, and q. For example, p 0, n 0, d 5, q 2 satisfies the equation, as does p 0, n 3, d 1, q 3, and other combinations. Thus, the number of dimes is not determined. (201, 205)

Let x average speed. We add the times and distances; then, using the rate formula, (x)(1) 25, so x 25 mi/hr. (201, 202)

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45.


48.


Let x qts of original solution Let r rate for return.

Amounts of solution and of alcohol may be added.

46.

(40%) (2 x) 2 0.30x; so 0.8 0.4x 2.0 0.30x; thus, x 12. (201, 204)

Let s average overall rate.


(approximately).

(131⁄2) (s) 600; thus, s 600 131⁄2 44.4

49.

(201, 202)


(time expressed in kilowatt-hours, or kwh) Let t number of kwh. This problem must be broken up into two different parts: (1) finding the total power or the total number of kilowatt-hours (kwh) used, and (2) calculating the charge for that amount. (1) Total power used, t (900w) (5 hr) (100w) (25 hr) (5w) (400 hr) (4,500 2,500 2,000) watt-hours 9,000 watt-hours. One thousand watt-hours equals one kilowatt-hour. Thus, t 9 kilowatt-hours, so that the charge is (8¢)(9) 72¢. (201, 205) 47.


Interest first year equals rate principal 5 %

$100 $5. New principal $105.00. Interest second year rate new principal 5 % $105 $5.25. Final principal $105.00 $5.25 $110.25. (201, 205) 50.


Let r cost per inch of cloth. 30¢ 5¢ From the table, r 36 in 30¢; r . 36 in 6 in 5 Thus, 96r 96 80¢. (201, 205) 6

(Net in out.) Let x time to fill the tub completely. Since only 9 gallons are needed (there are already 1 (201) 3 in the tub), we have 1 x 9, so x 6. 2

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Area, Perimeter, and Volume Problems

301. Formula Problems. Here, you are given certain data about one or more geometric figures, and you are asked to supply some missing information. To solve this type of problem, follow this procedure: STEP 1. If you are not given a diagram, draw your own; this may make the answer readily apparent or may suggest the best way to solve the problem. You should try to make your diagram as accurate as possible, but do not waste time perfecting your diagram. STEP 2. Determine the formula that relates to the quantities involved in your problem. In many cases it will be helpful to set up tables containing the various data. (See Sections 303–316.) STEP 3. Substitute the given information for the unknown quantities in your formulas to get the desired answer. When doing volume, area, and perimeter problems, keep this hint in mind: Often the solutions to such problems can be expressed as the sum of the areas or volumes or perimeters of simpler figures. In such cases do not hesitate to break down your original figure into simpler parts. In doing problems involving the following figures, these approximations and facts will be useful: 2 is approximately 1.4. 2 sin 45° 2 which is approximately 0.71. 3 is approximately 1.7. is approximately 3.16. 10

3 2

sin 60° which is approximately 0.87.

p is approximately 272 or 3.14. sin 30° 12 Example: The following figure contains a square, a right triangle, and a semicircle. If ED CD and the length of CD is 1 unit, find the area of the entire figure.

Solution: To calculate the area of the entire figure, we calculate the areas of the triangle, square, and semicircle and then add these together. In a right triangle, the area is

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1 ab where a and b are the sides of the triangle. In this case we will call side ED, a and side 2 1 1 CD, b. ED CD 1, so the area of the triangle is (1) (1), or . 2 2 The area of a square is s2, where s is a side. We see that the side EC of the square is the hypotenuse of the right triangle. We can calculate this length by using the formula c2 a2 b2 where a b 1; then we can see that c 2 . Thus, in this case, s 2 so the area of the square is ( 2 )2 2. 1 AB is the diameter of the semicircle, so AB is the radius. Since all sides of a square are 2 1 1 equal, AB 2 , and the radius is 2 . Further, the area of a semicircle is p r2 where r 2 2 2 1 1 1 is the radius, so the area of this semicircle is p 2 p. 2 2 4

The total area of the whole figure is equal to the area of the triangle plus the area of the 1 1 1 1 square plus the area of the semicircle 2 p 2 p. 2 4 2 4 Example: If water flows into a rectangular tank with dimensions of 12 inches, 18 inches, and 30 inches at the rate of 0.25 cubic feet per minute, how long will it take to fill the tank? Solution: This problem is really a combination of a rate problem and a volume problem. First we must calculate the volume, and then we must substitute in a rate equation to get our final answer. The formula for the volume of a rectangular solid is V lwh where l, w, and h are the length, width, and height, respectively. We must multiply the three dimensions of the tank to get the volume. However, if we look ahead to the second part of the problem, we see that we want the volume in cubic feet; therefore we convert 12 inches, 18 inches, and 30 inches to 1 foot, 1.5 feet, and 2.5 feet, respectively. Multiplying gives us a volume of 3.75 cubic feet. Now substituting in the equation: rate time volume, we get 3.75 0.25 time 3.75; time ; thus, the time is 15 minutes. 0.25 302. Comparison problems. Here you are asked to identify the largest, or smallest, of a group of figures, or to place them in ascending or descending order of size. The following procedure is the most efficient one: STEP 1. Always diagram each figure before you come to any conclusions. Whenever possible, try to include two or more of the figures in the same diagram, so that their relative sizes are most readily apparent. STEP 2. If you have not already determined the correct answer, then (and only then) determine the size of the figures (as you would have done in Section 301) and compare the results. (Note that even if Step 2 is necessary, Step 1 should eliminate most of the possible choices, leaving only a few formula calculations to be done.) Example: Which of the following is the greatest in length? (A) (B) (C) (D) (E)

The perimeter of a square with a side of 4 inches. The perimeter of an isosceles right triangle whose equal sides are 8 inches each. The circumference of a circle with a diameter of 4 2 inches. The perimeter of a pentagon whose sides are all equal to 3 inches. The perimeter of a semicircle with a radius of 5 inches.

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Solution: Diagramming the five figures mentioned, we obtain the following illustration:

From the diagram, it is apparent that the square and the pentagon are both smaller than the circle. Further observation should show that the circle is smaller than the triangle. Thus we need only to see which is larger—the semicircle or the triangle. The perimeter of the semicircle is found by the formula: P 2r pr (the sum of the diameter and the semicircular arc, where r is the radius). Since r in this case is 5 inches, the perimeter is approximately 10 (3.14)5, or 25.7 inches. The formula for the perimeter of a triangle is the sum of the sides. In this case, two of the sides are 8 inches and the third side can be found by using the relationship c2 a2 b2, where a and b are the sides of a right triangle, and c is the hypotenuse. Since in our problem a b 8 inches, c 82 82 128 2(64) 8 2 , which is the third side of the triangle. The perimeter is 8 8 8 2 , which is 16 8 2 . This is approximately equal to 16 8(1.4) or 27.2, so the triangle is the largest of the figures.

FORMULAS USED IN AREA, PERIMETER, AND VOLUME PROBLEMS It is important that you know as many of these formulas as possible. Problems using these formulas appear frequently on tests of all kinds. You should not need to refer to this table when you do problems. Learn these formulas before you go any further.

303. Square. The area of a square is the square of one of its sides. Thus, if A represents the area, and s represents the length of a side, A s2. The area of a square is also one-half of the 1 square of its diagonal and may be written as A d 2, where d represents the length of a 2 diagonal. The perimeter of a square is 4 times the length of one of its sides, or 4s.

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304. Rectangle. Let a and b represent the length of two adjacent sides of a rectangle, and let A represent the area. Then the area of a rectangle is the product of the two adjacent sides. A ab. The perimeter, P, is the sum of twice one side and twice the adjacent side. P 2a 2b.

305. Parallelogram. The area of a parallelogram is the product of a side and the altitude, h, to that side. A bh (in this case the altitude to side b). The area can also be expressed as the product of two adjacent sides and the sine of the included angle: A ab sin c, where c is the angle included between side a and side b. The perimeter is the sum of twice one side and twice the adjacent side. P 2a 2b. Let a and b represent the length of 2 adjacent sides of a parallelogram. Then, c is the included angle. But A represents its area, P its perimeter, and h the altitude to one of its sides.

306. Triangle. The area of any triangle is one-half of the product of any side and the altitude 1 to that side. A bh, where b is a side, and h the altitude to that side. The area may be 2 written also as one-half of the product of any two adjacent sides and the sine of the included 1 angle. A ab sin C, where A is the area, a and b are two adjacent sides, and C is the included 2 angle. The perimeter of a triangle is the sum of the sides of the triangle. P a b c, where P is the perimeter, and c is the third side.

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Right triangle. The area of a right triangle is one-half of the product of the two sides 1 adjacent to the right angle. A ab, where A is the area, and a and b are the adjacent sides. 2 The perimeter is the sum of the sides. P a b c, where c is the third side, or hypotenuse. 307.

Equilateral triangle. The area of an equilateral triangle is one-fourth the product of a 1 3 . A s2 3 , where A is the area, and s is one of the equal sides. The side squared and 4 perimeter of an equilateral triangle is 3 times one side. P 3s, where P is the perimeter. 308.

NOTE: The equilateral triangle and the right triangle are special cases of the triangle, and any law that applies to the triangle applies to both the right triangle and to the equilateral triangle.

309. Trapezoid. The area of a trapezoid is one-half of the product of the altitude and the sum 1 of the bases. A h(B b), where A is the area, B and b are the bases, and h is their altitude. 2 The perimeter is the sum of the 4 sides. P B b c d, where P is the perimeter, and c and d are the other 2 sides.

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310. Circle. The area of a circle is p (pi) times the square of the radius. A pr2, where A is the area, and r is the radius. The circumference is pi times the diameter or pi times twice the radius. C pd 2pr, where C is the circumference, d the diameter, and r the radius.

311. Semicircle. The area of a semicircle is one-half pi times the square of the radius. 1 A pr 2, where A is the area, and r is the radius. The length of the curved portion of the 2 1 semicircle is one-half pi times the diameter or pi times the radius. C pd pr, where C is the 2 circumference, d is the diameter, and r is the radius. The perimeter of a semicircle is equal to the 1 circumference plus the length of the diameter. P C d pd d, where P is the perimeter. 2

312. Rectangular solid. The volume of a rectangular solid is the product of the length, width, and height. V lwh, where V is the volume, l is the length, w is the width, and h is the height. The volume is also the product of the area of one side and the altitude to that side. V Bh, where B is the area of its base and h the altitude to that side. The surface area is the sum of the area of the six faces. S 2wh 2hl 2wl, where S is the surface area.

313. Cube. The volume of a cube is its edge cubed. V e3, where V is the volume and e is an edge. The surface area is the sum of the areas of the six faces. S 6e2, where S is the surface area.

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314. Cylinder. The volume of a cylinder is the area of the base times the height. V Bh, where V is the volume, B is the area of the base, and h is the height. Note that the area of the base is the area of the circle pr 2, where r is the radius of a base. The surface area not including the bases is the circumference of the base times the height. S1 Ch 2pr h, where S1 is the surface area without the bases, C the circumference, and h the height. The area of the bases 2pr 2. Thus, the area of the cylinder, including the bases, S2 2prh 2pr 2 2pr(h r).

4 315. Sphere. The volume of a sphere is four-thirds p times the cube of the radius. V pr 3, 3 where V is the volume and r is the radius. The surface area is 4p times the square of the radius. S 4pr 2, where S is the surface area.

316. Hemisphere. The volume of a hemisphere is two-thirds p times the cube of the radius. 2 V pr 3 where V is the volume and r is the radius. The surface area not including the area 3 of the base is 2p times the square of the radius. S1 2pr 2, where S1 is the surface area without the base. The total surface area, including the base, is equal to the surface area without the base plus the area of the base. S2 2pr 2 pr 2 3pr 2, where S2 is the surface area including the base.

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317. Pythagorean Theorem. The Pythagorean Theorem states a very important geometrical relationship. It states that in a right triangle, if c is the hypotenuse (side opposite the right angle), and a and b are sides adjacent to the right angle, then c2 a2 b2.

Examples of right triangles are triangles with sides of 3, 4, and 5, or 5, 12, and 13. Any multiples of these numbers also form right triangles—for example, 6, 8, and 10, or 30, 40, 50. Using the Pythagorean Theorem to find the diagonal of a square we get d 2 s2 s2 or d 2 2s2, where d is the diagonal and s is a side. Therefore, d s 2, or the diagonal of a square is 2 times the side.

318. Another important fact to remember in doing area problems is that areas of two similar (having the same shape) figures are in the same ratio as the squares of corresponding parts of the figures. Example: Triangles P and Q are similar. Side p of triangle P is 2 inches, the area of triangle P is 3 square inches, and corresponding side q of triangle Q is 4 inches. What is the area of triangle Q?

Solution: The square of side p is to the square of side q as the area of P is to the area of Q. If we call x the area of triangle Q, then we get the following relationship: The square of side p is to the square of side q as the area of P is to the area of Q, or 22 3 3 4 2 or 4 x x 16 Therefore, x 12 square inches.

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Practice Test 3 Area, Perimeter, and Volume Problems Correct answers and solutions follow each test. 1.

A

B

C

D

E

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1. Which of the following figures has the largest area?

(A) (B) (C) (D) (E) 2.

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B

C

D

E

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2. If the area of the base of a rectangular solid is tripled, what is the percent increase in its

volume? (A) (B) (C) (D) (E)

3.

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B

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E

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is 12 by 13 ?

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it take to fill the tank, which measures 18 32 27?

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E

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less than one minute less than two minutes, but not less than one minute less than three minutes, but not less than two minutes less than four minutes, but not less than three minutes four minutes or more

5. The ratio of the area of a circle to the radius of the circle is

(A) (B) (C) (D) (E) 6.

22 yards 24 yards 27 yards 36 yards 46 yards

4. If water flows into a rectangular tank at the rate of 6 cubic feet per minute, how long will

(A) (B) (C) (D) (E) 5.

200 % 300 % 600 % 800 % 900 %

3. How many yards of a carpeting that is 26 inches wide will be needed to cover a floor that

(A) (B) (C) (D) (E) 4.

a square with a perimeter of 12 inches a circle with a radius of 3 inches a right triangle with sides of 3, 4, and 5 inches a rectangle with a diagonal of 5 inches a regular hexagon with a perimeter of 18 inches

p 2p p2 4p 2 not determinable

6. Which of the following figures has the smallest perimeter or circumference?

(A) (B) (C) (D) (E)

a circle with a diameter of 2 feet a square with a diagonal of 2 feet a rectangle with sides of 60 and 4 feet a pentagon with each side equal to 16 inches a hexagon with each side equal to 14 inches

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7.

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7. In the figure shown, DE is parallel to BC. If the area of triangle ADE is half that of

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trapezoid DECB, what is the ratio of AE to AC? (A) (B) (C) (D) (E)

8.

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E

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8. At a speed of 22 revolutions per minute, how long will it take a wheel of radius 10 ,

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22 rolling on its edge, to travel 10 feet? (Assume p equals , and express answer to 7 nearest 0.1 second.) (A) (B) (C) (D) (E)

9.

10.

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E

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(A) (B) (C) (D) (E)

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0.2 seconds 0.4 seconds 5.2 seconds 6.3 seconds 7.4 seconds

9. If the diagonal of a square is 16 long, what is the area of the square?

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1:2 1 : 2 1:3 1 : 3 1 : 3 1

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10.

64 square inches 642 square inches 128 square inches 128 2 square inches 256 square inches

In the diagram shown, ACDF is a rectangle, and GBHE is a circle. If CD 4 inches, and AC 6 inches, what is the number of square inches in the shaded area?

(A) (B) (C) (D) (E)

16 – 4p square inches 24 – 4p square inches 24 – 16p square inches 16 – 2p square inches 24 – 2p square inches

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11.

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11. What is the area of an equilateral triangle with a side of 1 inch?

(A) 1 square inch 3 (B) square inch 2 1 (C) square inch 2 3 (D) square inch 4 1 (E) square inch 3

12.

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12. The measurements of a rectangle are 12 feet by 16 feet. What is the area of the smallest

circle that can cover this rectangle entirely (so that no part of the rectangle is outside the circle)? (A) (B) (C) (D) (E)

13.

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E

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3 4 his room is a rectangle, measuring 12 feet by 18 feet, how many such tiles will he need?

13. A man wishes to cover his floor with tiles, each one measuring inch by 2 inches. If

(A) (B) (C) (D) (E) 14.

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192 square feet 384 square feet 100p square feet 128p square feet 400p square feet

144 1,152 1,728 9,216 20,736

14. The volume of a sphere is equal to the volume of a cylinder. If the radius of the sphere

is 4 miles and the radius of the cylinder is 8 miles, what is the height of the cylinder? (A) 8 miles 4 (B) miles 3 (C) 4 miles 16 (D) miles 3 (E) 1 mile

15.

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22 7

15. A wheel travels 33 yards in 15 revolutions. What is its diameter? (Assume p .)

(A) (B) (C) (D) (E)

0.35 feet 0.70 feet 1.05 feet 1.40 feet 2.10 feet

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16.

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16. If a rectangle with a perimeter of 48 inches is equal in area to a right triangle with legs

of 12 inches and 24 inches, what is the rectangle’s diagonal? (A) (B) (C) (D) (E)

17.

18.

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22 a square piece of cloth with a side of 8? (Use p .) 7 (A) 25.5 square inches (B) 54.4 square inches (C) 56.8 square inches (D) 142.1 square inches (E) 284.2 square inches

18. A container is shaped like a rectangular solid with sides of 3 inches, 3 inches, and 11

inches. What is its approximate capacity, if 1 gallon equals 231 cubic inches?

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B

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E

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while the 30-inch-diameter wheels of another car travel at a rate of 18 revolutions per minute. What is the ratio of the speed of the second car to that of the first?

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1:1 3:2 4:3 6:5 9:8

20. A circular garden twenty feet in diameter is surrounded by a path three feet wide.

What is the area of the path? (A) (B) (C) (D) (E)

21.

14 ounces 27 ounces 55 ounces 110 ounces 219 ounces

19. The 20-inch-diameter wheels of one car travel at a rate of 24 revolutions per minute,

(A) (B) (C) (D) (E) 20.

1 2

17. What is the approximate area that remains after a circle 3 in diameter is cut from

(A) (B) (C) (D) (E) 19.

12 inches 122 inches 123 inches 24 inches The answer cannot be determined from the given information.

9p square feet 51p square feet 60p square feet 69p square feet 90p square feet

21. What is the area of a semicircle with a diameter of 16 inches?

(A) (B) (C) (D) (E)

32p square inches 64p square inches 128p square inches 256p square inches 512p square inches

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22.

23.

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22. If the edges of a cube add up to 4 feet in length, what is the volume of the cube?

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(A) (B) (C) (D) (E) 23.

64 cubic inches 125 cubic inches 216 cubic inches 512 cubic inches None of these.

The inside of a trough is shaped like a rectangular solid, 25 feet long, 6 inches wide, and filled with water to a depth of 35 inches. If we wish to raise the depth of the water to 38 inches, how much water must be let into the tank? 25 (A) cubic feet 96 25 (B) cubic feet 8 75 (C) cubic feet 2 (D) 225 cubic feet (E) 450 cubic feet

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25.

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24.

If one gallon of water equals 231 cubic inches, approximately how much water will fill 22 a cylindrical vase 7 inches in diameter and 10 inches high? (Assume p .) 7 (A) 1.7 gallons (B) 2.1 gallons (C) 3.3 gallons (D) 5.3 gallons (E) 6.7 gallons

25. Tiles of linoleum, measuring 8 inches 8 inches, cost 9¢ apiece. At this rate, what will

it cost a man to cover a floor with these tiles, if his floor measures 10 feet by 16 feet? (A) (B) (C) (D) (E)

26.

27.

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$22.50 $25.00 $28.00 $32.40 $36.00

26. Which of the following figures has the largest area?

(A) (B) (C) (D) (E) 27.

a 3 : 4 : 5 triangle with a hypotenuse of 25 inches a circle with a diameter of 20 inches a square with a 20-inch diagonal a regular hexagon with a side equal to 10 inches a rectangle with sides of 10 inches and 30 inches

If the radius of the base of a cylinder is tripled, and its height is divided by three, what is the ratio of the volume of the new cylinder to the volume of the original cylinder? (A) (B) (C) (D) (E)

1:9 1:3 1:1 3:1 9:1

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28.

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28.

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If one cubic foot of water equals 7.5 gallons, how long will it take for a faucet that flows at a rate of 10 gal/min to fill a cube 2 feet on each side (to the nearest minute)? (A) (B) (C) (D) (E)

29.

30.

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29. The ratio of the area of a square to the square of its diagonal is which of the following?

(A) (B) (C) (D) (E)

A

B

C

D

E

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2:1 2: 1 1:1 1 : 2 1:2

30. If ABCD is a square, with side AB 4 inches, and AEB and CED are semicircles, what

is the area of the shaded portion of the diagram below? (A) (B) (C) (D) (E)

31.


31.

8 – p square inches 8 – 2p square inches 16 – 2p square inches 16 – 4p square inches 16 – 8p square inches

If the area of a circle is equal to the area of a rectangle, one of whose sides is equal to p, express the other side of the rectangle, x, in terms of the radius of the circle, r. xr x pr x r2 x r 1 (E) x r

(A) (B) (C) (D)

32.

A

B

C

D

E

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32.

If the volume of a cube is 27 cubic meters, find the surface area of the cube. (A) (B) (C) (D) (E)

9 square meters 18 square meters 54 square meters 3 square meters 1 square meter

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33.

A

B

C

D

E

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33. What is the area of a regular hexagon one of whose sides is 1 inch?

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3 3 (A) 4 (B) 3 3 3 (C) 2 (D) 3 (E) 6

34.

35.

36.

37.

A

B

C

D

E

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A

B

C

D

E

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A

B

C

D

E

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A

B

C

D

E

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34.

What is the area of the triangle pictured below? (A) (B) (C) (D) (E)

35.

18 square units 32 square units 24 square units 12 square units 124 square units

If a wheel travels 1 mile in 1 minute, at a rate of 600 revolutions per minute, what is 22 the diameter of the wheel, in feet? (Use p .) 7 (A) 2.2 feet (B) 2.4 feet (C) 2.6 feet (D) 2.8 feet (E) 3.0 feet

36. Which of the following figures has the largest perimeter?

(A) (B) (C) (D) (E) 37.

a square with a diagonal of 5 feet a rectangle with sides of 3 feet and 4 feet an equilateral triangle with a side equal to 48 inches a regular hexagon whose longest diagonal is 6 feet a parallelogram with sides of 6 inches and 7 feet

A man has two containers: The first is a rectangular solid, measuring 3 inches 4 inches 10 inches; the second is a cylinder having a base with a radius of 2 inches and a height of 10 inches. If the first container is filled with water, and then this water is poured into the second container, which of the following occurs? (A) (B) (C) (D) (E)

There is room for more water in the second container. The second container is completely filled, without overflowing. The second container overflows by less than 1 cubic inch. The second container overflows by less than 2 (but not less than 1) cubic inches. The second container overflows by 2 or more cubic inches.

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38.

A

B

C

D

E

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38. If, in this diagram, A represents a square with a side of 40, and B, C, D, and E are semi-

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circles, what is the area of the entire figure? (A) (B) (C) (D) (E)

39.

40.

A

B

C

D

E

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A

B

C

D

E

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39. The area of a square is 81p2. What is the length of the square’s diagonal?

(A) (B) (C) (D) (E) 40.

42.

A

B

C

D

E

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A

B

C

D

E

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41.

A

B

C

D

E

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43.

a square with a diagonal of 10 inches a 3-4-5 right triangle with a hypotenuse of 15 inches a pentagon, each of whose sides is 5 inches a right isosceles triangle with an area of 72 square inches a regular hexagon with a radius of 5 inches

If you double the area of the base of a rectangular solid, and also triple the solid’s height, what is the ratio of the new volume to the old volume? (A) (B) (C) (D) (E)

43.

$70 $125 $480 $630 None of these.

Which of the following has the largest perimeter? (A) (B) (C) (D) (E)

42.

9p 9p2 18p 9p2 18p2

The following diagram represents the floor of a room that is to be covered with carpeting at a price of $2.50 a square yard. What will be the cost of the carpeting? (A) (B) (C) (D) (E)

41.

16 4p square inches 16 8p square inches 16 16p square inches 16 32p square inches 16 64p square inches

2:3 3:2 1:6 6:1 None of these.

A certain type of linoleum costs $1.50 per square yard. If a room measures 27 feet by 14 feet, what will be the cost of covering it with linoleum? (A) (B) (C) (D) (E)

$44.10 $51.60 $63.00 $132.30 $189.00

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44.

A

B

C

D

E

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44. How many circles, each with a 4-inch radius, can be cut from a rectangular sheet of

paper, measuring 16 inches 24 inches?

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(A) (B) (C) (D) (E) 45.

A

B

C

D

E

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6 7 8 12 24

45. The ratio of the area of an equilateral triangle, in square inches, to its perimeter, in

inches, is (A) 3 : 4 (B) 4 : 3 (C) 3 : 4 (D) 4 : 3 (E) The answer cannot be determined from the given information.

46.

A

B

C

D

E

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46.

What is the volume of a cylinder whose radius is 4 inches, and whose height is 10 inches? (Assume that p 3.14.) (A) (B) (C) (D) (E)

47.

48.

A

B

C

D

E

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A

B

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D

E

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47.

The area of a square is 144s2. What is the square’s diagonal? (A) (B) (C) (D) (E)

48.

A

B

C

D

E

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49.

A

B

C

D

E

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50.

50 cubic feet 50p cubic feet 125p cubic feet 250p cubic feet 500p cubic feet

A certain type of carpeting is 30 inches wide. How many yards of this carpet will be needed to cover a floor that measures 20 feet by 24 feet? (A) (B) (C) (D) (E)

50.

12s 12s 2 24s 144s 144s2

A circular pool is ten feet in diameter and five feet deep. What is its volume, in cubic feet? (A) (B) (C) (D) (E)

49.

125.6 cubic inches 134.4 cubic inches 144.0 cubic inches 201.2 cubic inches 502.4 cubic inches

48 64 144 192 None of these.

Two wheels have diameters of 12 inches and 18 inches, respectively. Both wheels roll along parallel straight lines at the same linear speed until the large wheel has revolved 72 times. At this point, how many times has the small wheel revolved? (A) (B) (C) (D) (E)

32 48 72 108 162

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Answer Key for Practice Test 3 1. B

14. B

27. D

39. B

2. A

15. E

28. C

40. A

3. B

16. B

29. E

41. D

4. B

17. B

30. B

42. D

5. E

18. C

31. C

43. C

6. B

19. E

32. C

44. A

7. D

20. D

33. C

45. E

8. C

21. A

34. D

46. E

9. C

22. A

35. D

47. B

10. B

23. B

36. D

48. C

11. D

24. A

37. A

49. B

12. C

25. D

38. B

50. D

13. E

26. B

the original height of the figure, we have the formula Vo hoBo. The new volume, V is equal to 3hoBo. Thus, the new volume is three times the original volume—an increase of 200 %. (301) 3.

4.

Choice B is correct. First we must calculate the volume of the tank in cubic feet. Converting the 1 dimensions of the box to feet, we get 1 feet

2 2 1 3 2 feet 2 feet, so the total volume is

3 4 2 8 9 , or 9, cubic feet. Thus, at a rate of 6 cubic feet 3 4 9 1 per minute, it would take , or 1 minutes to fill 6 2 the tank. (312, 201)

5.

Choice E is correct. Here, we use the formula A pr 2, where A area, and r radius. Thus, A the ratio of A to r is just p r. Since r is not a r constant, the ratio cannot be determined. (310)

6.

Choice B is correct. First, we diagram the circle and the square and see that the square has a smaller perimeter. Next, we notice that the circle, which has a larger circumference than the square, has circumference 2p, or about 6.3 feet. But the perimeters of the rectangle (9 feet), of the pentagon (5 16 inches 80 inches 6 feet, 8 inches), and of the hexagon (6 14 inches 84 inches 7 feet) are all greater than the circumference of the circle, and therefore also greater than the perimeter of the square. Thus, the square has the smallest perimeter. (302)

7.

Choice D is correct. The formula involved here is A1 : A2 s12 : s22, where A1 represents the area of the triangle with one side of length s1, and A2


Choice B is correct. This is a fairly difficult comparison problem, but the use of diagrams simplifies it considerably.

From diagram A it is apparent that the circle is larger than the square. Diagram B shows that the circle is larger than the right triangle. And, since a rectangle with a diagonal of 5 inches is made up of two right triangles, as shown in diagram C, the circle is larger than the rectangle. Finally, as shown in diagram D, the circle is larger than the hexagon. Thus, the circle is the largest of the five figures described. (302) 2.

Choice A is correct. This is a formula problem: letting Vo represent the original volume, Bo represent the original area of the base, and ho represent

Choice B is correct. Here, we must find the length of carpeting needed to cover an area of 12 13 , or 156 square feet. The formula needed is: A lw, where l length and w width, both expressed in feet. Now, since we know that A 156 square feet, 26 and w 26 inches, or feet, we can calculate l as 12 26 156 , or 72 feet. But since the answer must 12 be expressed in yards, we express 72 feet as 24 yards. (304)

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represents the area of the triangle corresponding to s2. If we let s1 represent AE, and s2 represent AC, so that A1 is the area of ADE and A2 is the area AE of ABC, then we have the resulting formula AC s1 A1 . The area of the trapezoid DEBC is twice s A2 2

the area of ADE, or 2A1, so the area of ABC is equal to the sum of the area of ADE and DECB, which equal A1 and 2A1, respectively; thus, the area of ABC is 3A1. So, A1 : A2 1 : 3. Thus, s1 : s2

13 1 : 3.

area of the circle is p(2 inches)2, or 4p square inches. Subtracting, we obtain the area of the shaded portion: 24 – 4p square inches. (304, 310) 11. Choice D is correct. We use the formula for the

3 s2 , where s is a area of an equilateral triangle, 4 3 side. If s 1, then the area of the triangle is . 4 (308)

(318) 12. Choice C is correct. An angle, which is inscribed in

8. Choice C is correct. Since the radius of the circle is

10 inches, its circumference is 2p (10 inches), or 22 440 2 (10 inches), which equals inches. This is 7 7 the distance the wheel will travel in one revolution. To travel 10 feet, or 120 inches, it must travel 440 21 120 , or revolutions. At a speed of 22 7 11 11 revolutions per minute, or revolutions per sec30 21 11 630 ond, it will take or seconds. Carrying 11 30 121 the division to the nearest tenth of a second, we get 5.2 seconds. (310)

a circle, whose sides cut off an arc of 180° (that is, intersects the ends of a diameter) is a right angle. According to the Pythagorean Theorem, the diameter AC, being the hypotenuse of a triangle with sides of 12 feet and 16 feet, has a length of 122 162 400 20 feet. Therefore, if we call d the diameter, the area of the circle is d 2 20 2 A p p 100p square feet. 2 2

9. Choice C is correct. If we let d represent the diag-

onal of a square, s represent the length of one side, and A represent its area, then we have two formulas: d s 2, and A s2, relating the three quantities. However, from the first equation, we d2 can see that s2 , so we can derive a third 2 d2 formula, A , relating A and d. We are given 2 that d equals 16, so we can calculate the value of (16 inches)2 A as , or 128 square inches. 2

(303)

(310) 13. Choice E is correct. The area of the room 12

feet 18 feet 216 square feet. The area of one 3 3 tile inches 2 inches square inches. The 4 2 number of tiles area of the room area of one 216 144 square inches 216 square feet tile 3 3 square inch square inch 2 2 48 2 (304) 216

144 20,736 tiles. 3

10. Choice B is correct. The area of the shaded figure

is equal to the difference between the areas of the rectangle and the circle. The area of the rectangle is defined by the formula A bh, where b and h are the two adjacent sides of the rectangle. In this case, A is equal to 4 inches 6 inches, or 24 square inches. The area of the circle is defined by the formula A pr2, where r is the radius. Since BE equals the diameter of the circle and is equal to 4 inches, then the radius must be 2 inches. Thus, the

14. Choice B is correct. The volume of a sphere is found

4 by using the formula pr 3 where r is the radius. 3 In this case, the radius is 4 miles, so the volume is 256 p cubic miles. This is equal to the volume of a 3 256 cylinder of radius 8 miles so p p82h, since 3 the volume of a cylinder is p r 2 h, where h is the

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256p height, and r is the radius of the base. Solving 3 16 256

16 4 1 256p p82h; miles. 3 12 3 p64

3 4 (314, 315) p64

circumference, which equals 24 20 inches p 480p inches per minute. The speed of the second is 18 30 inches p 540p inches per minute. Thus, their ratio is 540p : 480p 9 : 8. (310) 20. Choice D is correct. The area of the path is equal to

15. Choice E is correct. 33 yards 99 feet 15 revolu-

99 33 tions. Thus, 1 revolution feet feet 6.6 15 5 feet. Since 1 revolution the circumference of the wheel, the wheel’s diameter circumference p. 22 6.6 feet 2.10 feet. 7

(310)

16. Choice B is correct. The area of the right triangle is

1 equal to ab where a and b are the legs of the 2 1 triangle. In this case, the area is 12 24, or 2 144 square inches. If we call the sides of the rectangle x and y we get 2x 2y 48, or y 24 x. The area of the rectangle is xy, or x(24 x). This must be equal to 144, so we get the equation 24x x2 144. Rearranging the terms gives us x2 24x 144 0, or (x 12)2. Since y 24 x, y 24 12, or y 12. This is satisfied only by x 12. By the Pythagorean Theorem we get: diagonal 1 2 2 12 2 1 44 1 44 2(144) 12 2 . (304, 306, 317) 17. Choice B is correct. The area of the square is 64

square inches, since A s2 where s is the length of a side, and A is the area. The area of the circle

7 16 8 9.625.

7 is p 4

2

22

49

77

Subtracting,

64 9.625 54.375 54.4 (approximately). (304, 310)

the area of the ring between two concentric circles of radii 10 feet and 13 feet. This area is obtained by subtracting the area of the smaller circle from the area of the larger circle. The area of the larger circle is equal to p its radius squared p(13)2 feet2 169p square feet. By the same process, the area of the smaller circle 100p square feet. The area of the shaded part 169p 100p 69p square feet. (310)

21. Choice A is correct. The diameter 16 inches, so

the radius 8 inches. Thus, the area of the whole circle p(8 inches)2 64p square inches. The area of the semicircle is one-half of the area of the whole circle, or 32p square inches. (311)

22. Choice A is correct. A cube has twelve equal

1 edges, so the length of one side of the cube is 12 of 4 feet, or 4 inches. Thus, its volume is 4 inches

4 inches 4 inches 64 cubic inches. (313)

18. Choice C is correct. The capacity of the volume

(V lwh, where l, w, h, are the adjacent sides of the solid) of the container (3 inches) (3 inches) (11 inches) 99 cubic inches; since 1 gallon equals 231 99 cubic inches, 99 cubic inches equal gallons 231 3 (the fraction reduces to ). One gallon equals 128 7 ounces (1 gallon 4 quarts, 1 quart 2 pints, 1 384 pint 16 ounces), so the container holds 7 ounces 55 ounces (approximately). (312) 19. Choice E is correct. The speed of the first wheel is

equal to its rate of revolution multiplied by its

23. Choice B is correct. The additional water will take

the shape of a rectangular solid measuring 25 feet

6 inches 3 inches (3″ the added depth) 1 1 25 25 cubic feet cubic feet. (312) 2 4 8

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COMPLETE SAT MATH REFRESHER • 239 24. Choice A is correct. The volume of the cylinder

22 7 pr 2h (10) cubic inches 385 cubic 7 2 inches. 231 cubic inches 1 gallon, so 385 cubic 385 5 inches gallons gallons 1.7 gallons 231 3 (approximately). (314) 2

25. Choice D is correct. The area of floor 10 feet

16 feet 160 square feet. Area of one tile 8 64 inches 8 inches 64 square inches 144 4 square feet square feet. Thus, the number of 9 4 tiles area of floor area of tile 160 360. 9 At 9¢ apiece, the tiles will cost $32.40. (304)

diagonal is 2s2. Thus, the ratio of the area of the square to the square of the diagonal is s2 : 2s2 or 1 : 2. (303) 30. Choice B is correct. The area of the square ABCD

is equal to 4 inches 4 inches 16 square inches. The two semicircles can be placed together diameter-to-diameter to form a circle with a radius of 2 inches, and thus, an area of 4p. Substracting the area of the circle from the area of the square, we obtain the combined areas of AED and BEC. But, since the figure is symmetrical, AED and BEC must be equal, so the area of AED is one-half of this remainder, which equals 16 4p, or 8 2p square inches. (303, 310) 31. Choice C is correct. The area of the circle is equal

26. Choice B is correct. Looking at the following three

diagrams, we can observe that the triangle, square, and hexagon are all smaller than the circle.

to pr 2, and the area of the rectangle is equal to px. Since these areas are equal, pr 2 px, and x r 2. (304, 310) 32. Choice C is correct. The volume of a cube is e3

where e is the length of an edge. If the volume is 27 cubic meters, then e3 27 and e 3 meters. The surface area of a cube is 6e2, and if e 3 meters, then the surface area is 54 square meters. (313) 33. Choice C is correct. The area of a regular hexagon,

Comparing the areas of the circle and the rectangle, we notice that the area of the circle is p (10 inches)2 100p square inches, which is greater than (10 inches)(30 inches) 300 square inches, the area of the rectangle. (p is approximately 3.14.) (302)

one of whose sides is 1 inch, is equal to the sum of the areas of 6 equilateral triangles, each with a side of 1 inch. The area of an equilateral triangle with a 3 side of 1 inch is equal to square inches. (The 4 formula for the area of an equilateral triangle with 3 a side of s is A s2 .) The sum of 6 such trian4 63 33 (308) gles is , or . 4 2

27. Choice D is correct. In a cylinder, V pr 2h, where

r is the radius of the base, and h is the height. The h new volume, V′ p(3r)2 3pr 2h 2V. Thus, 3 the ratio of the new volume to the old volume is 3 : 1. (314)

28. Choice C is correct. A cube 2 feet on each side has

a volume of 2 2 2 8 cubic feet. Since 1 cubic foot equals 7.5 gallons, 8 cubic feet equals 60 gallons. If the faucet flows at the rate of 10 gallons/ minute it will take 6 minutes to fill the cube. (313) 29. Choice E is correct. Let s the side of the square.

Then, the area of the square is equal to s2. The diagonal of the square is s 2 , so the square of the

34. Choice D is correct. The area of a triangle can be

1 expressed as ab sin C where a and b are any two 2 sides and C is the angle between them. In this case a 6, b 8, and C 30°. You should 1 remember that the sine of 30° is so the area is 2 1 1 (6)(8) 12. (307) 2 2

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240 • COMPLETE SAT MATH REFRESHER 35. Choice D is correct. Since the wheel takes 1 minute

40. Choice A is correct. We can regard the area as a

to make 600 revolutions and travels 1 mile in that time, we have the relation 1 mile 5,280 feet 600 5,280 revolutions. Thus, 1 revolution feet 8.8 600 22 feet circumference p(diameter) (diam7 22 eter). Therefore, the diameter 8.8 feet 7

rectangle, 20 ft 14 ft, with two rectangles, measuring 4 ft 6 ft and 2 ft 2 ft, cut out. Thus, the area is equal to 280 sq ft 24 sq ft 4 sq ft 252 252 sq ft sq yd 28 sq yds. ( Remember, 1 square 9 yard equals 9 square feet.) At $2.50 a square yard, 28 square yards will cost $70. (304)

2.8 feet.

(310)

36. Choice D is correct. In this case, it is easiest to cal-

culate the perimeters of the 5 figures. According to the Pythagorean Theorem, a square with a diag5 onal of 5 feet has a side of , which is equal to 2 52 . (This is found by multiplying the numerator 2 5 and denominator of by 2 .) If each side of 2 52 the square is , then the perimeter is 2 2 52

4 10 2 feet. A rectangle with sides of 2

3 feet and 4 feet has a perimeter of 2(3) 2(4), or 14 feet. An equilateral triangle with a side of 48 inches, or 4 feet, has a perimeter of 12 feet. A regular hexagon whose longest diagonal is 6 feet has a side of 3 feet and, therefore, a perimeter of 18 feet. (See the diagram for Solution 33.) Finally, a 1 parallelogram with sides of 6 inches, or foot, and 2 7 feet has a perimeter of 15 feet. Therefore, the hexagon has the largest perimeter. (302, 317) 37. Choice A is correct. The volume of the first con-

tainer is equal to 3 inches 4 inches 10 inches, or 120 cubic inches. The volume of the second container, the cylinder, is equal to pr 2h p(2 inches)2 (10 inches), or 40p cubic inches, which is greater than 120 cubic inches (p is greater than 3). So the second container can hold more than the first. If the first container is filled and the contents poured into the second, there will be room for more water in the second. (312, 314) 38. Choice B is correct. The area of the square is 16

square inches. The four semicircles can be added to form two circles, each of radius 2 inches, so the area of each circle is 4p square inches, and the two circles add up to 8p square inches. Thus, the total area is 16 8p square inches. (303, 311) 39. Choice B is correct. Since the area of the square is

81p2, one side of the square will equal 9p. According to the Pythagorean Theorem, the diagonal will equal 2 81p 81p2 9p2 . (303, 317)

41. Choice D is correct. The perimeter of the square is

1 equal to four times its side; since a side is , 2 2 or times the diagonal, the perimeter of the 2 , which is square in question is 4 5 2 202 approximately equal to 28.28 inches. The perimeter of a right triangle with sides that are in a 345 ratio, i.e., 9 inches, 12 inches, and 15 inches is 9 12 15 36 inches. The perimeter of the pentagon is 5 5 inches, or 25 inches. The perimeter of the right isosceles triangle (with sides of 12 inches, 12 inches, and 122 inches) is 24 122 inches, which is approximately equal to 40.968 inches. The perimeter of the hexagon is 6 5 inches, or 30 inches. Thus, the isosceles right triangle has the largest perimeter of those figures mentioned. You should become familiar with the approximate value of 2 , which is 1.414. (302)

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COMPLETE SAT MATH REFRESHER • 241 42. Choice D is correct. For rectangular solids, the fol-

lowing formula holds: V Ah, where A is the area of the base, and h is the height. If we replace A by 2A, and h by 3h, we get V (2A) (3h) 6V. Thus, V : V 6 :1. (312)

46. Choice E is correct. The formula for volume of a

cylinder is V r 2h, where r is the radius of the base, and h is the height. Here, r 4 inches, and h 10 inches, while p 3.14. (The symbol means “approximately equal to.”) Thus V (4)2(10)(3.14) 160(3.14) 502.4 cubic inches. (314) 47. Choice B is correct. If the area of a square is 144s2,

43. Choice C is correct. The area of the room is 27

feet 14 feet 378 square feet. 9 square feet 1 square yard, so the area of the room is 42 square yards. At $1.50 per square yard the linoleum to cover the floor will cost $63.00. (304)

then one side will equal 12s, so the diagonal will equal 12s 2 . (The Pythagorean Theorem may be 2 , used here to get d 144s 144s2 where d is the diagonal.) (303, 317) 48. Choice C is correct. The inside of the pool forms a

44. Choice A is correct. A circle with a 4-inch radius

has an 8-inch diameter, so there can be only 2 rows of 3 circles each, or 6 circles. (310)

cylinder of radius 5 feet, and height 5 feet. The volume is p r 2 h, or p 5 5 5 125p cubic feet. (314) 49. Choice B is correct. The area of the floor is 20 feet

1

24 feet 480 square feet. 30 inches is equal to 2 2 feet, and we must find the length which, when 1 multiplied by 2 feet, will yield 480 square feet. 2 This length is 192 feet, which equals 64 yards (3 feet 1 yard). (304) 50. Choice D is correct. The circumference of the larger

45. Choice E is correct. Let one side of the triangle

s2 3 be s. Then the area of the triangle is . 4 (Either memorize this formula or remember that it is derived by drawing an altitude to divide the triangle into two congruent 30°: 60°: 90° right triangles.) The perimeter of the equilateral triangle is 3s, so the ratio of the area to the perimeter is s23 : 3s, or s : 43 , which cannot be determined 4 unless we know the value of s. (308)

wheel is 18p inches (C pd). After 72 revolutions, the larger wheel will have gone a distance of 72(18p) inches. Since the smaller wheel moves at the same linear speed, it will also have gone 72(18p) inches. The circumference of the smaller wheel is 12p inches, and if we call the number of revolutions that the smaller wheel makes, r, then we know that 12pr 72(18p). Dividing both sides by 12p gives us r 6(18) or 108 revolutions. Note that in this problem we have used the relation, distance rate

time, where the time for both wheels is a fixed quantity. (310)

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Algebra Problems

Algebraic Properties Algebra is the branch of mathematics that applies the laws of arithmetic to symbols that represent unknown quantities. The most commonly used symbols are the letters of the alphabet such as A, B, C, x, y, z, etc. These symbols can be added, subtracted, multiplied, and divided like 6x numbers. For example, 3a 2a 5a, 2x x x, 3(5b) 15b, 2. These symbols can 3x be raised to powers like a3 or y2. Remember that raising a number to a power means multiplying the number by itself a number of times. For example, a3 a • a • a. The power is 3, and a is multiplied by itself 3 times. Generally, in algebra, a variable (an unknown represented by a symbol) appears in an equation (a statement that defines the relationship between certain quantities), and values of the variable that satisfy the equation must be found. For example, the equation 6a 12 is satisfied when the variable, a, is equal to 2. This section is a discussion on how to solve complicated algebraic equations and other related topics.

Fundamental Laws of Our Number System Following is a list of laws that apply to all the numbers necessary to work with when doing arithmetic and algebra problems. Remember these laws and use them in doing problems. 401. If x y and y z, then x z. This is called transitivity. For example, if a 3 and b 3, then a b. 402. If x y, then x z y z, and x z y z. This means that the same quantity can be added to or subtracted from both sides of an equation. For example, if a b, then add any number to both sides, say 3, and a 3 b 3. Or if a b, then a 3 b 3. 403. If x y, then x • z y • z and x z y z, unless z 0 (see Section 404). This means that both sides of an equation can be multiplied by the same number. For example, if a n, then 5a 5n. It also means that both sides of an equation can be divided by the same nonzero a b number. If a b, then . 3 3 404. Never divide by zero. This is a very important fact that must be remembered. The quotie nt of any quantity (except zero) divided by zero is infinity. 405. x y y x, and x • y y • x. Therefore, 2 3 3 2, and 2 • 3 3 • 2. Remember that this does not work for division and subtraction. 3 2 does not equal 2 3; and 3 2 does not equal 2 3. The property described above is called commutativity.

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Equations 406. Linear equation in one unknown. Equations with one variable are linear equations in one unknown. The variable is always in the first power, i.e., x or y or a, but never in a higher or fractional power, i.e., x2, y3, or a1/2. Examples of linear equations in one unknown are x 5 7, 3a 2 7a 1, 2x 7x 8 x, 8 4y, etc. To solve these equations, follow these steps: STEP 1. Combine the terms on the left and right sides of the equality. That is, (1) add all of the numerical terms on each side, and (2) add all of the terms with variables on each side. For example, if you have 7 2x 9 4x 3 2x 7 6x, combining terms on the left gives you 16 2x, because 7 9 16, and 2x is the only variable term on that side. On the right we get 8x 4, since 4x 2x 6x 8x and 3 7 4. Therefore the new equation is 16 2x 8x 4. STEP 2. Put all of the numerical terms on the right side of the equation and all of the variable terms on the left side. This is done by subtracting the numerical term on the left from both sides of the equation and by subtracting the variable term on the right side from both sides of the equation. In the example 16 2x 8x 4, subtract 16 from both sides and obtain 2x 8x 12; then subtracting 8x from both sides gives 6x 12. STEP 3. Divide both sides by the coefficient of the variable. In this case, where 6x 12, dividing by 6 gives 2. This is the final solution to the problem. Example: Solve for a in the equation 7a 4 2a 18 17a 10. Solution: From Step 1, we combine terms on both sides to get 5a 4 28 17a. As in Step 2, we then subtract 4 and 17a from both sides to give 12a 24. By Step 3, we then divide both sides of the equation by the coefficient of a, which is 12, to get a 2. Example: Solve for x in 2 x 6 0. Solution: Here Step 1 is eliminated because there are no terms to combine on either side. Step 2 requires that 6 be subtracted from both sides to get 2x 6. Then dividing by 2 gives x 3. 407. Simultaneous equations in two unknowns. These are problems in which two equations, each with two unknowns, are given. These equations must be solved together (simultaneously) in order to arrive at the solution. STEP 1. Rearrange each equation so that both are in the form that has the x term on the left side and the y term and the constant on the right side. In other words, put the equations in the form Ax By C where A, B, and C are numerical constants. For example, if one of the equations is 9x 10y 30 11y 3x 6, then subtract 10y and 30 from both sides to get 9x 21y 3x 36. Subtracting 3 x from both sides gives 6x 21y 36, which is in the form of Ax By C. The first equation should be in the form Ax By C, and the second equation should be in the form Dx Ey F where A, B, C, D, E, and F are numerical constants. STEP 2. Multiply the first equation by the coefficient of x in the second equation (D). Multiply the second equation by the coefficient of x in the first equation (A). Now the equations are in the form ADx BDy CD and ADx AEy AF. For example, in the two equations 2x 7y 12 and 3x y 1, multiply the first by 3 and the second by 2 to get 6x 21y 36 and 6x 2y 2. STEP 3. Equate the right sides of both equations. This can be done because both sides are equal to ADx. (See Section 401 on transitivity.) Thus, BDy CD AEy AF. So 21y 36 and 2y 2 are both equal to 6x and are equal to each other: 21y 36 2y 2. STEP 4. Solve for y. This is done in the manner outlined in Section 406. In the equation 21y AF CD 36 2y 2, y 2. By this method y . BD AE

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STEP 5. Substitute the value of y into either of the original equations and solve for x. In the B AF CD C E AF CD E general equations we would then have either x , or x . A BD AE A D BD AE D

In the example, if y 2 is substituted into either 2x 7y 12 or 3x y 1, then 2x 14 12 or 3x 3 can be solved to get x 1. Example: Solve for a and b in the equation 3a 4b 24 and 2a b 11. Solution: First note that it makes no difference in these two equations whether the variables are a and b instead of x and y. Subtract 4b from the first equation and b from the second equation to get the equations 3a 24 4b and 2a 11 b. Multiply the first by 2 and the second by 3. Thus, 6a 48 8b and 6a 33 3b. Equate 48 8b and 33 3b to get 48 8b 33 3b. Solving for b in the usual manner gives us b 3. Substituting the value of b 3 into the equation 3a 4b 24 obtains 3a 12 24. Solving for a gives a 4. Thus the complete solution is a 4 and b 3. Quadratic equations. Quadratic equations are expressed in the form ax2 bx c 0; 1 where a, b, and c are constant numbers (for example, , 4, 2, etc.) and x is a variable. An 2 equation of this form may be satisfied by two values of x, one value of x, or no values of x. Actually when there are no values of x that satisfy the equation, there are only imaginary solutions. These will not be dealt with. To determine the number of solutions, find the value of the expression b2 4ac where a, b, and c are the constant coefficients of the equation ax2 bx c 0. 408.

If solutions exist, they can be found by using the formulas: b ac b2 4 b ac b2 4 x and x 2a 2a Note that if b2 4ac 0, the two above solutions will be the same and there will be one solution. Example: Determine the solutions, if they exist, to the equation x2 6x 5 0. Solution: First, noting a 1, b 6, and c 5, calculate b2 4ac, or 62 4(1)(5). Thus, b2 4ac 16. Since this is greater than 0, there are two solutions. They are, from the formulas: 2 4 2 4 •1•5 •1•5 6 6 6 6 x and x 2•1 2•1

Simplify these to: 6 l6 6 16 x and x 2 2 6 4 2 6 4 10 As 16 4, x and x . Thus, the two solutions are x 1 2 2 2 2 and x 5. Another method of solving quadratic equations is to factor the ax2 bx c into two expressions. This will be explained in the next section. 409. Factoring. Factoring is breaking down an expression into two or more expressions, the product of which is the original expression. For example, 6 can be factored into 2 and 3 because

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2 • 3 6. x2 x can be factored into x and (x 1) because x2 x x(x 1). Then, if x2 bx c is factorable, it will be factored into two expressions in the form (x d) and (x e). If the expression (x d) is multiplied by the expression (x e), their product is x2 (d e)x de. For example, (x 3) • (x 2) equals x2 5x 6. To factor an expression such as x2 6x 8, find a d and e such that d e 6 and de 8. Of the various factors of 8, we find that d 4 and e 2. Thus x2 6x 8 can be factored into the expressions (x 4) and (x 2). Below are factored expressions. x2 2x 1 (x 1)(x 1)

x2 3x 2 (x 2)(x 1)

x2 4x 4 (x 2)(x 2)

x2 5x 6 (x 3)(x 2)

x2 4x 3 (x 3)(x 1)

x2 4x 5 (x 5)(x 1)

x2 10x 16 (x 8)(x 2)

x2 4x 5 (x 5)(x 1)

x2 5x 6 (x 2)(x 3)

x2 x 6 (x 3)(x 2)

An important rule to remember in factoring is that a2 b2 (a b)(a b). For example, x2 9 (x 3)(x 3). To apply factoring in solving quadratic equations, factor the quadratic expression into two terms and set each term equal to zero. Then, solve the two resulting equations. Example: Solve x2 x 6 0. Solution: First factor the expression x2 x 6 into x 3 and x 2. Setting each of these equal to 0 gives x 3 0 and x 2 0. Solving these equations gives us x 3 and x 2.

Algebra of Graphs 410a. Number Lines. Numbers, positive and negative, can be represented as points on a straight line. Conversely, points on a line can also be represented by numbers. This is done by

–4

–3

–2

1

–1 – 2 0

1 2

1

2

3

4

use of the number line. The diagram above is an example of a number line. On a number line, a point is chosen to represent the number zero. Then a point that is 1 unit to the right of 0 represents 1; a point that is 1⁄2 unit to the right of 0 is 1⁄2; a point that is 2 units to the right of 0 is 2; and so on. A point that is 1 unit to the left of 0 is 1; a point that is 1⁄2 unit to the left of 0 is 1⁄2; a point that is 2 units to the left of 0 is 2; and so on. As you can see, all points to the right of the 0 point represent positive numbers, and all those to the left of the 0 point represent negative numbers. To find the distance between two points on the line: 1. Find the numbers that represent the points. 2. The distance is the smaller number subtracted from the larger.

B –4

–3

A –2

–1

0

1

2

3

4

For example: Find the distance between point A and point B on the number line.

Point A is 2 on the number line and point B is 3. 2 is larger than 3, so the distance is 2(3) or +2 3 5. By counting the number of units between A and B, the distance is also found to be 5.

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410b. Coordinate geometry. These problems deal with the algebra of graphs. A graph consists of a set of points whose position is determined with respect to a set of axes usually labeled the X-axis and the Y-axis and divided into appropriate units. Locate a point on the graph with an “x coordinate” of a units and a “y coordinate” of b units. First move a units along the X axis (either to the left or right depending on whether a is positive or negative). Then move b units along the Y axis (either up or down depending on the sign of b). A point with an x coordinate of a, and a y coordinate of b, is represented by (a,b). The points (2,3), (1,4), (2,3), and (4,2) are shown on the following graph.

411. Distance between two points. If the coordinates of point A are (x1, y1) and the coordinates of point B are (x2,y2), then the distance on the graph between the two points is )2 ( y2 y1 )2. d (x2 x 1 Example: Find the distance between the point (2,3) and the point (5,1). Solution: In this case x1 2, x2 5, y1 3, and y2 1. Substituting into the above formula gives us 2 [13)] 2 42 25 ) ( 2 3 5 d (5 2

Note: This formula is a consequence of the Pythagorean Theorem. Pythagoras, an ancient Greek mathematician, discovered that the square of the length of the hypotenuse (longest side) of a right triangle is equal to the sum of the square of the lengths of the other two sides. See Sections 317 and 509. 412. Midpoint of the line segment joining two points. If the coordinates of the first point are (x1, y1) and the coordinates of the second point are (x2,y2), then the coordinates of the midpoint x1 x2 y1 y2 will be , . In other words, each coordinate of the midpoint is equal to the 2 2 average of the corresponding coordinates of the endpoints.

Example: Find the midpoint of the segment connecting the points (2,4) and (6,2).

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Solution: The average of 2 and 6 is 4 so the first coordinate is 4. The average of 4 and 2 is 26 42 3; thus the second coordinate is 3. The midpoint is (4,3). 4, 3 2 2

413. Plotting the graph of a line. An equation that can be put in the form of y mx b, where m and b are numerical constants can be represented as a line on a graph. This means that all of the points on the graph that the line passes through will satisfy the equation. Remember that each point has an x and a y value that can be substituted into the equation. To plot a line, follow the steps below: STEP 1. Select two values of x and two values of y that will satisfy the equation. For example, in the equation y 2x 4, the point (x 1, y 6), will satisfy the equation as will the point (x 2, y 0). There are an infinite number of such points on a line. STEP 2. Plot these two points on the graph. In this case, the two points are (1,6) and (2,0). These points are represented below.

STEP 3. Draw a line connecting the two points. This is the line representing the equation.

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(Note: A straight line is completely specified by two points.) Example: Graph the equation 2y 3x 12. Solution: Two points that satisfy this equation are (2,3) and (0,6). Plotting these points and drawing a line between them gives:

414. Y-intercept. The Y-intercept of a line is the point where the line crosses the Y-axis. At any point where a line, crosses the Y-axis, x 0. To find the Y-intercept of a line, simply substitute x 0 into the equation of the line, and solve for y. Example: Find the Y-intercept of the equation 2x 3y 6. Solution: If x 0 is substituted into the equation, it simplifies to 3y 6. Solving for y gives y 2. Thus, 2 is the Y-intercept. If an equation can be put into the form of y mx b, then b is the Y-intercept.

415. X-intercept. The point where a line intersects the X-axis is called the X-intercept. At this point y 0. To find the X-intercept of a line, substitute y 0 into the equation and solve for x. Example: Given the equation 2x 3y 6, find the X-intercept. Solution: Substitute y 0 into the equation getting 2x 6. Solving for x, find x 3. Thus the X-intercept is 3. In the diagram below, the Y- and X-intercepts of the equation 2x 3y 6 are illustrated.

416. Slope. The slope of a line is the change in y caused by a 1 unit increase in x. If an equation is in the form of y mx b, then as x increases 1 unit, y will increase m units. Therefore the slope is m.

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Example: Find the slope of the line 2x 3y 6. Solution: First put the equation into the form of y mx b. Subtract 2x from both sides 2 2 and divide by 3. The equation becomes y x 2. Therefore the slope is . 3 3

y2 y1 . The slope of the line joining two points, (x1, y1) and (x2, y2), is given by the expression m12 x1 x2 Example: Find the slope of the line joining the points (3,2) and (4,1). 3 Solution: Substituting into the above formula gives us m 3 where x1 3, 1 x2 4, y1 2, y2 1. 417. Graphing simultaneous equations. Recall that simultaneous equations are a pair of equations in two unknowns. Each of these equations is graphed separately, and each is represented by a straight line. The solution of the simultaneous equations (i.e., the pair of values that satisfies both at the same time) is represented by the intersection of two lines. Now, for any pair of lines, there are three possible relationships: 1. The lines intersect at one and only one point; in this case, this point represents the unique solution to the pair of equations. This is most often the case. Such lines are called consistent. 2. The lines coincide exactly, this represents the case where the two equations are equivalent ( just different forms of the same mathematical relation). Any point that satisfies either of the two equations automatically satisfies both. 3. The lines are parallel and never intersect. In this case the equations are called inconsistent, and they have no solution at all. Two lines that are parallel will have the same slope. Example: Solve graphically the equations 4x y 5 and 2x 4y 16. Solution: Plot the two lines represented by the two equations. (See Section 413.) The graph is shown below. Y

5 4

y = − 1−2 x + 4

(2,3)

3 2 1 −5 −4 −3 −2 −1

X

1 −1 −2

2

3

4

5

y = 4x − 5

−3 −4 −5

The two lines intersect in the point (2,3), which represents the solution x 2 and y 3. This can be checked by solving the equations as is done in Section 407. Example: Solve x 2y 6 and 2x 4y 8. Solution: Find two points that satisfy each equation. Draw a line connecting these two points. The two graphs will look like this:

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Y

5 4 3

(2x + 4y = 8) y = − 1−2 x + 2

(x + 2y = 6) y = − 1−2 x + 3

2 1 X

−6 −5 −4 −3 −2 −1

1 −1

2

3

4

5

6

−2 −3 −4 −5

These lines will never intersect, and these equations are termed inconsistent. There is no solution. Remember that two parallel lines have the same slope. This is an easy way to see whether two lines are consistent or inconsistent. Example: Find the solution to 2x 3y 8 and 4x 6y 16. Solution: On the graph these two lines are identical. This means that there are an infinite set of points that satisfy both equations. Identical lines are products of each other and can be reduced to the same equation. Y

2x − 3y = 8 4x = 6y + 16

4 3 2 1 −4 −3 −2 −1

1 2 3 4 −1 −2 −3 −4

X

418. Areas of polygons. Often, an elementary geometric figure is placed on a graph to calculate its area. This is usually simple for figures such as triangles, rectangles, squares, parallelograms, etc. Example: Calculate the area of the triangle in the figure below. Y (2,5)

(−2,1) −2 −1

4 3 2 1

(4,1) X

1 2 3 4

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1 Solution: The area of a triangle is (base)(height). On the graph the length of the line 2 joining (2,1) and (4,1) is 6 units. The height, which goes from point (2,5) to the base, 1 has a length of 4 units. Therefore the area is (6)(4) 12. 2 Example: Calculate the area of the square pictured below. Y

5 4 (0,3)

3 2 1

(4,0) X 1 2 3 4

Solution: The area of a square is given by the square of the side. To find this area first find the length of one side. The length of a segment whose endpoints are (x1,y1) and (x2, y2) is given by the formula (x2 x )2 ( y2 y1 )2 . Substituting in (0,3) and (4,0) gives a length 1 of 5 units. Thus the length of one side of the square is 5. Using the formula area (side)2 gives an area of 52 or 25 square units. To find the area of more complicated polygons, divide the polygon into simple figures whose areas can be calculated. Add these areas to find the total area.Example: Find the area of the figure below:

Solution: Divide the figure into two triangles and a rectangle by drawing vertical lines at (3,4) and (2,4). Thus the polygon is now two triangles and a rectangle.

1 The height of the left triangle is 4 units, and the base is 3. Using A bh gives the area as 6. 2 The height of the right triangle is 4, and the base is 4. The area is 8. The length of one side of the rectangle is 4, and the other side is 5. Using the formula, area base • height, gives the area as 20. Thus the total area is 6 8 20 34.

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Inequalities 419. Inequalities. These problems deal with numbers that are less than, greater than, or equal to other numbers. The following laws apply to all inequalities:

420. If equal quantities are added to both sides of an inequality, the direction of the inequality does not change. If x y, then x z y z and x z y z. If x y, then x z y z and x z y z. For example, given the inequality, 4 2, with 1 added to or subtracted from both sides, the results, 5 3 and 3 1, have the same inequality sign as the original. If the problem is algebraic, i.e., x 3 6, it is possible to subtract 3 from both sides to get this simple inequality x 3. 421.

Subtracting parts of an inequality from an equation reverses the order of the inequality. If x y, then z x z y. If x y, then z x z y.

For example, given that 3 5, subtracting 3 from the left-hand and 5 from the right-hand sides of the equation 10 10 results in 7 5. Thus the direction of the inequality is reversed. 422. Multiplying or dividing an inequality by a number greater than zero does not change the order of the inequality. y x If x y, and a 0, then xa ya and . a a y x If x y, and a 0, then xa ya and . a a For example, if 4 2, multiplying both sides by any arbitrary number (for instance, 5) gives 1 20 10, which is still true. Or, if algebraically 6h 3, dividing both sides by 6 gives h , which 2 is true. 423. Multiplying or dividing an inequality by a number less than 0 reverses the order of the inequality. y x If x y, and a 0, then xa ya and . a a y x If x y, and a 0, then xa ya and . a a If 3 2 is multiplied through by 2 it becomes 6 4, and the order of the inequality is reversed.

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Note that negative numbers are always less than positive numbers. Note also that the greater the absolute value of a negative number, the smaller it actually is. Thus, 10 9, 8 7, etc. 424. The product of two numbers with like signs is positive. If x 0 and y 0, then xy 0. If x 0 and y 0, then xy 0. For example, 3 times 2 is 6. 425. The product of two numbers with unlike signs is negative. If x 0 and y 0, then xy 0. If x 0 and y 0, then xy 0. For example, 2 times 3 is 6. 8 times 1 is 8, etc. 426. Linear inequalities in one unknown. In these problems a first power variable is given in an inequality, and this variable must be solved for in terms of the inequality. Examples of linear inequalities in one unknown are: 2x 7 4 x, 8y 3 2y, etc. STEP 1. By ordinary algebraic addition and subtraction (as if it were an equality) get all of the constant terms on one side of the inequality and all of the variable terms on the other side. In the inequality 2x 4 8x 16 subtract 4 and 8x from both sides and get 6x 12. STEP 2. Divide both sides by the coefficient of the variable. Important: If the coefficient of the variable is negative, you must reverse the inequality sign. For example, in 6x 12, dividing by 6 gives x 2. (The inequality is reversed.) In 3x 12 dividing by 3 gives x 4. Example: Solve for y in the inequality 4 y 7 9 2y. Solution: Subtracting 2y and 7 from both sides gives 6y 2. Dividing both sides by 6 1 gives y . 3 Example: Solve for a in the inequality 10 2a 0. Solution: Subtracting 10 from both sides gives 2a 10. Dividing both sides by 2 10 gives a or a 5. Note that the inequality sign has been reversed because of the 2 division by a negative number. 427. Simultaneous linear inequalities in two unknowns. These are two inequalities, each one in two unknowns. The same two unknowns are to be solved for in each equation. This means the equations must be solved simultaneously. STEP 1. Plot both inequalities on the same graph. Replace the inequality sign with an equality sign and plot the resulting line. The side of the line that makes the inequality true is then shaded in. For example, graph the inequality (2x y 4). First replace the inequality sign getting 2x y 4; then, plot the line. The X-intercept is 2. The Y-intercept is 4.

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To decide which side of the line satisfies the inequality, choose a convenient point on each side and determine which point satisfies the inequality. Shade in that side of the line. In this case, choose the point (0,0). With this point the equation becomes 2(0) 0 4 or 0 4. This is not true. Thus, shade in the other side of the line.

STEP 2. After both inequalities have been solved, the area that is common to both shaded portions is the solution to the problem. Example: Solve x y 2 and 3x 6. Solution: First graph x y 2 by plotting x y 2 and using the point (4,0) to determine the region where the inequality is satisfied:

Y

2

(4,0)

2

Graph the inequality 3x 6 on the same axes and get:

X

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6 5 4 3 2 1 −5 −4 −3 −2 −1

−1

1

2

3

4

5

X

−2 −3 −4 −5

The solution is the double shaded area. 428. Higher order inequalities in one unknown. These are inequalities that deal with variables multiplied by themselves. For example, x2 3 0, (x 1)(x 2) 4 and x3 7x 0 are such inequalities. The basic rules to remember in doing such problems are: 1. The product of any number of positive numbers is positive. 1 1 1 For example, 2 3 4 5 120, which is positive, or , which is positive. 2 2 4 2. The product of an even number of negative numbers is positive. For example, (3)(2) 6 or (3)(1)(9)(2) 54, which is positive. 3. The product of an odd number of negative numbers is negative. 1 For example, (1)(2)(3) 6 or ()(2)(3)(6)(1) 18. 2 4. Any number squared or raised to an even power is always positive or zero. For example, x2 0 or a4 0 for all x and for all a. Often these basic rules will make the solution to an inequality problem obvious. Example: Which of the following values can x2 not have? (A) 5

(B) 2

(C) 0

(D) 144

(E) 9

Solution: We know that x2 0 for all x so x2 cannot be negative. 2 is negative, so x2 cannot equal 2. The steps in solving a higher order inequality are: STEP 1. Bring all of the terms to one side of the inequality, making the other side zero. For example, in the inequality x2 3x 2, subtract 3x 2 from both sides to get x2 3x 2 0. STEP 2. Factor the resulting expression. To factor a quadratic expression means to write the

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original expression as the product of two terms in the 1st power, i.e., x2 x • x. x is a factor of x2. (See Section 409 for a detailed explanation of factoring.) The quadratic expression x2 3x 2 when factored is (x 2)(x 1). Note that x • x x2, 2x x 3x and ( 1) ( 2) 2. Most quadratic expressions can easily be factored by taking factors of the last term (in this case 2 and 1) and adding or subtracting them to x. Through trial and error the right combination is found. An important fact to remember when factoring is: (a b)(c d ) ac ad bc bd. Example: (x 4)(x 2) x2 4x 2x 8 x2 6x 8. Another is that a2 b2 (a b)(a b). Example: x2 16 (x 4)(x 4). STEP 3. Investigate which terms are positive and which terms are negative. For example, in (x 3) (x 2) 0, either (x 3) and (x 2) are both positive or (x 3) and (x 2) are both negative. If one were positive and the other were negative, the product would be negative and would not satisfy the inequality. If the factors are positive, then x 3 0 and x 2 0, which yields x 3 and x 2. For x to be greater than 3 and to be greater than 2, it must be greater than 3. If it is greater than 3 it is automatically greater than 2. Thus, with positive factors x 3 is the answer. If the factors are negative, x 3 0 and x 2 0, or x 2. For x to be less than 3 and less than 2 it must be less than 2. Thus, with negative factors x 2 is the answer. As both answers are possible from the original equation, the solution to the original problem is x 3 or x 2. Example: For which values of x is x2 5 6x? Solution: First subtract 6x from both sides to get x2 6x 5 0. The left side factors into (x 5)(x 1) 0. Now for this to be true one factor must be positive and one must be negative, i.e., their product is less than zero. Thus, x 5 0 and x 1 0 or x 5 0 and x 1 0. If x 5 0 and x 1 0 then x 5 and x 1, or 1 x 5. If x 5 0 and x 1 0 then x 5 and x 1, which is impossible because x cannot be less than 1 and greater than 5. Therefore, the solution is 1 x 5. Example: For what values of x is x2 4? Solution: Subtract 4 from both sides to get x2 4 0. Remember that a2 b2 (a b)(a b); thus x2 4 (x 2)(x 2). Hence, (x 2)(x 2) 0. For this to be true x 2 0 and x 2 0 or x 2 0 and x 2 0. In the first case x 2 and x 2 or 2 x 2. The second case is x 2 and x 2 is impossible because x cannot be less than 2 and greater than 2. Thus, the solution is 2 x 2. Example: When is (x2 1)(x 2)2 (x 3) greater than or equal to zero? Solution: This can be written as (x2 1)(x 2)2(x 3) 0. This is already in factors. The individual terms must be investigated. x2 1 is always positive because x2 0 so x2 1 must be greater than 0. (x 2)2 is a number squared so this is always greater than or equal to zero. Therefore, the product of the first two terms is positive or equal to zero for all values of x. The third term x 3 is positive when x 3, and negative when x 3. For the entire expression to be positive, x 3 must be positive, i.e., x 3. For the expression to be equal to zero, x 3 0, i.e., x 3, or (x 2)2 0, i.e., x 2. Thus, the entire expression is positive when x 3 and zero when x 2 or x 3.

Exponents and Roots 429. Exponents. An exponent is an easy way to express repeated multiplication. For example, 5 5 5 5 54. The 4 is the exponent. In the expression 73 7 7 7, 3 is the exponent. 73 means 7 is multiplied by itself three times. If the exponent is 0, the expression always has a value of 1. Thus, 60 150 1, etc. If the exponent is 1, the value of the expression is the number base. Thus, 41 4 and 91 9. In the problem 53 54, we can simplify by counting the factors of 5. Thus 53 54 53 4 7 5 . When we multiply and the base number is the same, we keep the base number and add the exponents. For example, 74 78 712.

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For division, we keep the same base number and subtract exponents. Thus, 88 82 882 8. 6

A negative exponent indicates the reciprocal of the expression with a positive exponent, 1 thus 32 . 32 430. Roots. The square root of a number is a number whose square is the original number. for example, 16 4, since 4 4 16. (The symbol always means a positive number.) To simplify a square root, we factor the number.

32 16 • 2 16 • 2 4 2 72 36 • 2 36 • 2 6 2 300 25 • 12 25 • 12 5 • 12 5 • 4 •3 5 4 3 5 • 2 3 10 3 We can add expressions with the square roots only if the numbers inside the square root sign are the same. For example, 3 7 2 7 5 7

18 2 9 • 2 2 9 2 2 3 2 2 4 2. 431. Evaluation of expressions. To evaluate an expression means to substitute a value in place of a letter. For example: Evaluate 3a2 c3; if a 2, c 3. 3a2 c3 3( 2)2 ( 3)3 3(4) ( 27) 12 27 39 Given: a b ab b2. Find: 2 3. Using the definition, we get 2 3 ( 2)(3) (3)2 69 23 3

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Practice Test 4 Algebra Problems Correct answers and solutions follow each test. 1.

A

B

C

D

E

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1.

For what values of x is the following equation satisfied: 3x 9 21 7x? (A) (B) (C) (D) (E)

2.

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B

C

D

E

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2.

What values may z have if 2z 4 is greater than z 6? (A) (B) (C) (D) (E)

3.

A

B

C

D

E

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3.

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E

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4.

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E

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5.

3 only 1 only 1 only 1 and 1 only 3, 1, and 1 only

If the coordinates of point P are (0,8), and the coordinates of point Q are (4,2), which of the following points represents the midpoint of PQ? (A) (B) (C) (D) (E)

5.

any values greater than 10 any values greater than 2 any values less than 2 any values less than 10 None of these.

If ax2 2x 3 0 when x 3, what value(s) can a have? (A) (B) (C) (D) (E)

4.

3 only 3 only 3 or 3 only no values an infinite number of values

(0,2) (2,4) (2,5) (4,8) (4,10)

In the formula V pr2h, what is the value of r, in terms of V and h? V (A) ph (B) p

V h

(C) pVh ph (D) V (E) 6.

A

B

C

D

E

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6.

V ph

Solve the inequality x2 3x 0. (A) (B) (C) (D) (E)

x 3 3 x 0 x3 0x3 3x

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7.

8.

A

B

C

D

E

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B

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7.

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Which of the following lines is parallel to the line represented by 2y 8x 32? (A) (B) (C) (D) (E)

8.

In the equation 4.04x 1.01 9.09, what value of x is necessary to make the equation true? (A) (B) (C) (D) (E)

9.

A

B

C

D

E

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9.

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E

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10.

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B

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D

E

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1 only 2 only 1 and 2 only 1 and 2 only any values between 1 and 2

What is the largest possible value of the following expression: (x 2)(3 x)(2 x)2(2x 6)(2x 4)? (A) (B) (C) (D) (E)

11.

1.5 0 1 2 2.5

What values of x satisfy the equation (x 1)(x 2) 0? (A) (B) (C) (D) (E)

10.

y 8x 32 y 8x 16 y 16x 32 y 4x 32 y 2x 16

11.


For what value(s) of k is the following equation satisfied: 2k 9 k 4k 6 3k? (A) 5 only (B) 0 only 5 (C) only 2 (D) no values (E) more than one value

12.

A

B

C

D

E

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12.

In the equation p aq2 bq c, if a 1, b 2, and c 1, which of the following expresses p in terms of q? (A) (B) (C) (D) (E)

p (q 2)2 p (q 1)2 p q2 p (q 1)2 p (q 2)2

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13.

A

B

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E

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13.

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If A B C 10, A B 7, and A B 5, what is the value of C? (A) 1 (B) (C) (D) (E)

14.

A

B

C

D

E

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14.

If 5x 15 is greater than 20, which of the following best describes the possible values of x? (A) (B) (C) (D) (E)

15.

A

B

C

D

E

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15.

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E

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16.

x must be greater than 5 x must be greater than 3 x must be greater than 1 x must be less than 5 x must be less than 1

t2 1 If 2, then what value(s) may t have? t1 (A) (B) (C) (D) (E)

16.

3 6 7 The answer cannot be determined from the given information.

1 only 1 only 1 or 1 no values an infinite number of values

If 4m 9n, what is the value of 7m, in terms of n? 63n (A) 4 9n (B) 28 7n (C) 9 28n (D) 9 7n (E) 4

17.

A

B

C

D

E

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17.

The coordinates of a triangle are (0,2), (2,4), and (1,6). What is the area of the triangle in square units (to the nearest unit)? (A) (B) (C) (D) (E)

2 square units 3 square units 4 square units 5 square units 6 square units

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18.

A

B

C

D

E

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18.

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1 In the formula s gt2, what is the value of t, in terms of s and g? 2 2s (A) g s g

(B) 2

s (C) 2g (D) (E) 19.

A

B

C

D

E

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19.

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20.

22.

23.

A

B

C

D

E

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A

B

C

D

E

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A

B

C

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E

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21.

(0,2), (0,2), (2,0) (1,3), (1,5), (3,4) (1,3), (1,7), (4,5) (2,2), (2,0), (1,1) (2,3), (2,5), (3,3)

a b must equal 8. a b must be between 2 and 6. a b must be between 3 and 5. a b must be between 5 and 8. a b must be between 5 and 11.

The area of a square will be doubled if: (A) (B) (C) (D) (E)

23.

0 x 60 0 x 150 60 x 180 120 x 180 120 x 150

If 2 a 5, and 6 b 3, what are the possible values of a b? (A) (B) (C) (D) (E)

22.

2s g

Which of the following sets of coordinates does not represent the vertices of an isosceles triangle? (A) (B) (C) (D) (E)

21.

In the triangle ABC, angle A is a 30° angle, and angle B is obtuse. If x represents the number of degrees in angle C, which of the following best represents the possible values of x? (A) (B) (C) (D) (E)

20.

s 2 g

The length of the diagonal is divided by 2. The length of the diagonal is divided by 2. The length of the diagonal is multiplied by 2. The length of the diagonal is multiplied by 2 . None of the above.

Find the value of y that satisfies the equation 8.8y 4 7.7y 7. (A) (B) (C) (D) (E)

1.1 7.7 8.0 10.0 11.0

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24.

25.

A

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24.

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Which of the following is a factor of the expression 2x2 1? (A) (B) (C) (D) (E)

25.

A businessman has ten employees; his salary is equal to six times the average of the employees’ salaries. If the eleven of them received a total of $64,000 in one year, what was the businessman’s salary that year? (A) (B) (C) (D) (E)

26.

27.

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26.

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28.

21 24 28 33 36

If 2p 7 is greater than 3p 5, which of the following best describes the possible values of p? (A) (B) (C) (D) (E)

28.

$4,000 $6,000 $24,000 $40,000 $44,000

If 6x 3 equals 15, what is the value of 12x 3? (A) (B) (C) (D) (E)

27.

x2 x2 x 2 x 2 None of these.

p must be greater than 2. p must be greater than 12. p must be less than 2. p must be less than 12. p must be greater than 2, but less than 12.

What is the value of q if x2 qx 1 0, if x 1? (A) (B) (C) (D) (E)

2 1 0 1 2

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29.

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29.

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What is the area (to the nearest unit) of the shaded figure in the diagram below, assuming that each of the squares has an area of 1? (A) (B) (C) (D) (E)

30.

31.

32.

33.

A

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30.

Which of the following statements is false? (A) Any two numbers, a and b, have a sum equal to a b. (B) Any two numbers, a and b, have a product equal to a • b. (C) Any two numbers, a and b, have a difference equal to a b. a (D) Any two numbers, a and b, have a quotient equal to . b (a b) (E) Any two numbers, a and b, have an average equal to . 2

31.

If (x 1) (x 2) (x2 4) 0, what are the possible values of x? (A) (B) (C) (D) (E)

32.

(A) (B) (C) (D) (E) 33.

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34.

2 only 2 only 1, 2, or 4 only 1, 2, or 4 only 1, 2, or 2 only

If P Q R, and P R 2Q, what is the ratio of P to R? 1:1 1:2 2:1 1:3 3:1

r 2 5r 6 For what value(s) of r is equal to 0? r2 (A) (B) (C) (D) (E)

34.

12 13 14 15 16

2 only 3 only 3 only 2 or 3 2 or 3

What is the value of a2b 4ab2 4b3, if a 15 and b 5? (A) (B) (C) (D) (E)

1,625 2,125 2,425 2,725 3,125

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35.

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35.

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If m 4n 2n 8m, what is the ratio of n to m? (A) (B) (C) (D) (E)

36.

If the value of a lies between 5 and 2, and the value of b lies between 7 and 1, what are the possible values for the product, a • b? (A) (B) (C) (D) (E)

37.

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38.

10.5 square units 12.5 square units 15.0 square units 20.0 square units 21.0 square units

If A B 12, and B C 16, what is the value of A C? (A) (B) (C) (D) (E)

39.

between 14 and 2 between 35 and 2 between 2 and 35 between 12 and 3 between 14 and 35

What is the area, in square units, of a triangle whose vertices lie on points (5,1), (5,4), and (2,4)? (A) (B) (C) (D) (E)

38.

1:4 1 : 4 4 : 1 2:7 7:2

4 28 4 28 The answer cannot be determined from the given information.

What is the solution to the equation x2 x 1 0? 1 3 1 3 (A) and 2 2 2 2 1 3 (B) only 2 2 (C)

1 3 only 2 2

(D) no real solutions (E) 0 40.

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40.

Which of the following equations will have a vertical line as its graph? (A) (B) (C) (D) (E)

xy1 xy1 x1 y1 xy 1

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41.

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41.

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For what values of x does x2 3x 2 equal zero? (A) (B) (C) (D) (E)

42.

If a b equals 12, and a b equals 6, what is the value of b? (A) (B) (C) (D) (E)

43.


For what values of m is m2 4 equal to 4m? (A) (B) (C) (D) (E)

44.

1 only 2 only 1 or 2 only 1 or 2 only None of these.

2 only 0 only 2 only 4 only more than one value

If x 0, and y 2, and x2yz 3xz2 y2z 3y 4x 0, what is the value of z? 4 (A) 3 3 (B) 2 3 (C) 4 4 (D) 3 (E) The answer cannot be determined from the given information.

45.

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45.

If c 4d 3c 2d, what is the ratio of c to d? (A) (B) (C) (D) (E)

46.

1:3 1 : 3 3:1 2:3 2 : 3

If 3 x 7, and 6 x 2, which of the following best describes x? (A) (B) (C) (D) (E)

2x6 2x7 3x6 3x7 No value of x can satisfy both of these conditions.

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47.

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47.

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What are the coordinates of the midpoint of the line segment whose endpoints are (4,9) and (5,15)? (A) (B) (C) (D) (E)

48.

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48.

t2 2t t If , what does t equal? 2t 4 2 (A) (B) (C) (D) (E)

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49.

2 only 2 only any value except 2 any value except 2 any value

If x y 4, and x z 9, what is the value of ( y z)? (A) (B) (C) (D) (E)

50.

(4,5) (5,9) (4,15) (4.5,12) (9,24)


Of the following statements, which are equivalent? I. 3 x 3 II. x2 9 1 1 III. x 3 (A) I and II only (B) I and III only (C) II and III only (D) I, II, and III (E) None of the above.

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Answer Key for Practice Test 4 1. A

14. C

27. D

39. D

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15. D

28. A

40. C

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32. D

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20. E

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34. E

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22. D

35. E

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10. C

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36. E

48. D

11. D

24. E

37. A

49. A

12. B

25. C

38. E

50. A

13. B

26. A

5.

V r2 ph Take the square root of both sides: r equals

2.

3.

Choice A is correct. The original equation is 3x 9 21 7x. First subtract 9 and 7x from both sides to get: 4x 12. Now divide both sides by the coefficient of x, 4, obtaining the solution, x 3. (406) Choice A is correct. Given 2z 4 x 6. Subtracting equal quantities from both sides of an inequality does not change the order of the inequality. Therefore, subtracting z and 4 from both sides gives a solution of z 10. (419, 420) Choice C is correct. Substitute 3 for x in the original equation to get the following: a(3)2 2(3) 3 0 9a 6 3 0 9a 9 0 a1

4.

(406)

Choice C is correct. To find the midpoint of the line segment connecting two points, find the point whose x-coordinate is the average of the two given x-coordinates, and whose y-coordinate is the average of the two given y-coordinates. The midpoint 04 82 here will be , , or (2,5). (412) 2 2

V . ph

(408)

6.

Choice D is correct. Factor the original expression into x(x 3) 0. In order for the product of two expressions to be less than 0 (negative), one must be positive and the other must be negative. Thus, x 0 and x 3 0; or x 0 and x 3 0. In the first case, x 0 and x 3. This is impossible because x cannot be less than 0 and greater than 3 at the same time. In the second case x 0 and x 3 which can be rewritten as 0 x 3. (428)

7.

Choice D is correct. Divide both sides of the equation 2y 8x 32 by 2 to get y 4x 16. Now it is in the form of y mx b, where m is the slope of the line and b is the Y intercept. Thus the slope of the line is 4. Any line parallel to this line must have the same slope. The answer must have a slope of 4. This is the line y 4x 32. Note that all of the choices are already in the form of y mx b. (416)

8.

Choice D is correct. Subtract 1.01 from both sides to give: 4.04x 8.08. Dividing both sides by 4.04 gives a solution of x 2. (406)

9.

Choice D is correct. If a product is equal to zero, then one of the factors must equal zero. If (x 1)(x 2) 0, either x 1 0, or x 2 0. Solving these two equations, we see that either x 1 or x 2. (408, 409)

10.

Choice C is correct. It is possible, but timeconsuming, to examine the various ranges of x, but it will be quicker if you realize that the same factors appear, with numerical multiples, more than once in the expression. Properly factored, the expression becomes:


Choice E is correct. Divide both sides of the equation by ph:

4(x 2) 4 (3 x) 2 (x 2)(2 x) 2 (2)(x 2) (3 x)(2)(3 x) Since squares of real numbers can never be negative, the whole product has only one negative term and is therefore negative, except when one of the terms is zero, in which case the product is also zero. Thus, the product cannot be larger than zero for any x. (428)

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11.

Choice D is correct. Combine like terms on both sides of the given equations and obtain the equivalent form: k 9 k 6. This is true for no values of k. If k is subtracted from both sides, 9 will equal 6, which is impossible. (406)

12.

Choice B is correct. Substitute for the given values of a, b, and c, and obtain p q2 2q 1; or, rearranging terms, p (q 1)2. (409)

13.

Choice B is correct. A B C 10. Also, A B 7. Substitute the value 7 for the quantity (A B) in the first equation and obtain the new equation: 7 C 10 or C 3. A B 5 could be used with the other two equations to find the values of A and B. (406)

14.

15.

16.

17.

The area of the rectangle ABEF (2)(4) 8 square units. 1 The area of the triangle ABC (1)(4) 2 square 2 units. 1 The area of the triangle CDE (1)(2) 1 square 2 unit. 1 The area of the triangle ADF (2)(2) 2 square 2 units. Thus the area of the triangle ACD 8 5 3 square units. (418) 18.

Choice C is correct. If 5x 15 20, then subtract 15 from both sides to get 5x 5. Now divide both sides by 5. This does not change the order of the inequality because 5 is a positive number. The solution is x 1. (419, 426)

1 Choice E is correct. Since s gt 2, divide both 2 1 sides of the equation by g to obtain the form, 2 2s 2 t . Then, after taking the square roots, t g 2s . g

(403)

Choice D is correct. Factor (t 2 1) to obtain the product (t 1)(t 1). For any value of t, except 1, the equation is equivalent to (t 1) 2, or t 1. One is the only possible value of t. However this value is not possible as t 1 would equal 0, and the t2 1 quotient would not be defined. (404, 409) t1

19.

Choice A is correct. The sum of the three angles of a triangle must be 180°. Since angle A is 30°, and angle B is between 90° and 180° (it is obtuse), their sum is greater than 120° and less than 180° (the sum of all three angles is 180°). Their sum subtracted from the total of 180° gives a third angle greater than zero, but less than 60°. (419)

9n Choice A is correct. If 4m 9n, then m . 4 Multiplying both sides of the equation by 7, we 63n (403) obtain: 7m . 4

20.

Choice E is correct. An isosceles triangle has two equal sides. To find the length of the sides, we use 2 the distance formula, (x x 1 )2 () y2 y1 . 2 In the first case the lengths of the sides are 4, 22 and 22 . Thus two sides have the same length, and it is an isosceles triangle. The only set of points that is not an isosceles triangle is the last one. (411)

21.

Choice E is correct. The smallest possible value of a is greater than 2, and the smallest possible value of b is greater than 3, so the smallest possible value of a b must be greater than 2 3 5. Similarly, the largest values of a and b are less than 5 and 6, respectively, so the largest possible of a b is less than 11. Thus, the sum must be between 5 and 11. (419)

22.

Choice D is correct. If the sides of the original square are each equal to s, then the area of the square is s2, and the diagonal is s2. Now, a new square, with an area of 2s2, must have a side of s2 . Thus, the diagonal is 2s, which is 2 times the original length of the diagonal. (302, 303)

23.

Choice D is correct. First place all of the variable terms on one side and all of the numerical terms on

Choice B is correct. As the diagram shows, the easiest way to calculate the area of this triangle is to start with the area of the enclosing rectangle and subtract the three shaded triangles.

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the other side. Subtracting 7.7y and adding 4 to both sides of the equation gives 1.1y 11. Now divide both sides by 1.1 to solve for y 10. (406) 24.

25.

Choice E is correct. To determine whether an expression is a factor of another expression, give the variable a specific value in both expressions. An expression divided by its factor will be a whole number. If we give x the value 0, then the expression 2x2 1 has the value of 1. x 2 then has the value of 2. 1 is not divisible by 2, so the first choice is not a factor. The next choice has the value of 2, also not a factor of 1. Similarly x 2 and x 2 take on the values of 2 and 2 , respectively, when x 0 and are not factors of 2x2 1. Therefore, the correct choice is (E). (409) Choice C is correct. Let x equal the average salary of the employees. Then the employees receive a total of 10x dollars, and the businessman receives six times the average, or 6x. Together, the eleven of them receive a total of 10x 6x 16x, which equals $64,000. Thus, x equals $4,000, and the businessman’s salary is 6x, or $24,000. (406)

26.

Choice A is correct. 6x 3 15, therefore 6x 12 and x 2. Substituting x 2 into the expression 12x 3, gives 24 3 which equals 21. (406)

27.

Choice D is correct. 2p 7 3p 5. To both sides of the equation add 5 and subtract 2p, obtaining 12 p. Thus, p is less than 12. (419, 426)

28.

Choice A is correct. Substituting 1 for x in the given equation obtains 1 q 1 0, or q 2 0. This is solved only for q 2. (406)

29.


The area of the shaded figure can most easily be found by taking the area of the square surrounding it (25), and subtracting the areas of the four triangles marked A (1), B (2), C (3), and D (6), leaving an area of 25 (1 2 3 6) 13 square units. (418) 30.

Choice D is correct. If the number b is equal to a zero, the quotient is not defined. For all other b pairs, all five statements are true. (401–405)

31.

Choice E is correct. If a product equals zero, one of the factors must be equal to zero also. Thus, either x 1 0, or x 2 0, or x2 4 0. The possible solutions, therefore, are x 1, x 2, and x 2. (408)

32.

Choice D is correct. Solve the equation P Q R, for Q (the variable we wish to eliminate), to get Q R P. Substituting this for Q in the second equation yields P R 2(R P) 2R 2P, or 1 P 3P R. Therefore, the ratio of P to R is , or . 3 R (406)

33.

Choice B is correct. The fraction in question will equal zero if the numerator equals zero, and the denominator is nonzero. The expression r 2 5r 6 can be factored into (r 2)(r 3). As long as r is not equal to 2 the equation is defined, and r 2 can be canceled in the original equation to yield r 3 0, or r 3. For r equals 2 the denominator is equal to zero, and the fraction in the original equation is not defined. (404, 409)

34.

Choice E is correct. This problem can be shortened considerably by factoring the expression a2b 4ab2 4b3 into the product (b)(a 2b)2. Now, since b 5, and (a 2b) 25, our product equals 5 25

25, or 3,125. (409)

35.

Choice E is correct. Subtract m 2n from both sides of the given equation and obtain the equivalent form, 2n 7m. Dividing this equation by 2m 7 n gives , the ratio of n to m. 2 m

(406)

36.

Choice E is correct. The product will be positive in the case: a positive and b positive, or a negative and b negative; and negative in the case: a positive and b negative, or a negative and b positive. Thus, the positive products must be (2) (1) and (5) (7). The largest positive value is 35. Similarly, the negative products are (5) (1) and (2) (7); and the most negative value that can be obtained is 14. Thus, the product falls between 14 and 35. (419)

37.

Choice A is correct. As can be seen from a diagram, this triangle must be a right triangle, since the line from (5,1) to (5,4) is vertical, and the line from (5,4) to (2,4) is horizontal. The lengths of these two perpendicular sides are 3 and 7, respectively. Since the area of a right triangle is half the product of the perpendicular sides, the area is equal to 1 3 7, or 10.5. (410, 418) 2

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38.

Choice E is correct. Solving the first equation for A gives A 12 B. Solving the second equation for C gives C 16 B. Thus, the sum A C is equal to 28 2B. There is nothing to determine the value of B, so the sum of A and C is not determined from the information given. (406)

39.

Choice D is correct. The value of b2 4ac determines the nature of the roots. From the equation substitute a 1, b 1, and c 1 into the expression. b2 4ac 1 4 3. As b2 4ac is negative, there are no real solutions to the equation. (408)

40.

Choice C is correct. If we graph the five choices we will get:

The only choice that is a vertical line is x 1. (413) 41.

Choice C is correct. The factors of x2 3x 2 are (x 1) and (x 2). Either x 1 0, or x 2 0. x may equal either 1 or 2. (408)

42.

Choice B is correct. a b 12 and a b 6. Rewrite these equations as a 12 b and a 6 b. 12 b and 6 b are both equal to a. Or, 12 b 6 b. Thus, 6 2b and b 3. (407)

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43.

Choice C is correct. Let m2 4 4m. Subtracting 4m from both sides yields m2 4m 4 0. Factor to get the following equation: (m 2)2 0. Thus, m 2 is the only solution. (408)

44.

Choice B is correct. Substitute for the given values of x and y, obtaining: (0)2(2)(z) (3)(0)(z)2 (2)2(z) (3)(2) (4)(0) 0. Perform the indicated multiplications, and combine terms. 0(z) 0(z 2 ) 4z 6 3 0 4z 6 0. This equation has z as its 2 only solution. (406)

45.

46.

47.

Choice C is correct. c 4d 3c 2d. Add 2d c to each side and get 6d 2c. (Be especially careful 6 3 c about your signs here.) Dividing by 2d: . 2 1 d Thus, c : d 3 : 1. (406) Choice C is correct. x must be greater than 3, less than 7, greater than 2, and less than 6. These conditions can be reduced as follows: If x is less than 6 it is also less than 7. Similarly, x must be greater than 3, which automatically makes it greater than 2. Thus, x must be greater than 3 and less than 6. (419) Choice D is correct. To obtain the coordinates of the midpoint of a line segment, average the corresponding coordinates of the endpoints. Thus, the 4 5 9 15 midpoint will be , or (4.5,12). (412) 2 2

48.

Choice D is correct. If both sides of the equation are multiplied by 2t 4, we obtain: t2 2t t2 2t, which is true for every value of t. However, when t 2, the denominator of the fraction on the left side of the original equation is equal to zero. Since division by zero is not a permissible operation, this fraction will not be defined for t 2. The equation cannot be satisfied for t 2. (404, 406, 409)

49.

Choice A is correct. If we subtract the second of our equations from the first, we will be left with the following: (x y) (x z) 4 9, or y z 5. (402)

50.

Choice A is correct. If x2 is less than 9, then x may take on any value greater than 3 and less than 3; other values will produce squares greater than or 1 1 equal to 9. If x is less than , x is restricted to 3 positive values greater than 3, and all negative values. For example, if x 1, then conditions I and II 1 are satisfied, but x equals 1, which is greater 1 than . 3

(419)

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Geometry Problems Basic Definitions 500. Plane geometry deals with points and lines. A point has no dimensions and is generally represented by a dot (.). A line has no thickness, but it does have length. Lines can be straight or curved, but here it will be assumed that a line is straight unless otherwise indicated. All lines have infinite length. Part of a line that has a finite length is called a line segment. Remember that the distance between two lines or from a point to a line always means the perpendicular distance. Thus, the distance between two lines pictured below is line A as this is the only perpendicular line. Also, the distance from a line to a point is the perpendicular from the point to the line. Thus, AB is the distance from point A to the line segment CBD.

501.

Angles. An angle is formed when two lines intersect at a point.

Angle B, angle ABC, B, ABC are all possible names for the angle shown.

The measure of the angle is given in degrees. If the sides of the angle form a straight line, then the angle is said to be a straight angle and has 180°. A circle has 360°, and a straight angle is a turning through a half circle. All other angles are either greater or less than 180°.

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Angles are classified in different ways: An acute angle has less than 90°.

A right angle has exactly 90°.

In the diagram, the small square in the corner of the angle indicates a right angle (90°).

An obtuse angle has between 90° and 180°.

A straight angle has exactly 180°.

A reflex angle has between 180° and 360°.

502. Two angles are complementary if their sum is 90°. For example, an angle of 30° and an angle of 60° are complementary. Two angles are supplementary if their sum is 180°. If one angle is 82°, then its supplement is 98°. 503. Vertical angles. These are pairs of opposite angles formed by the intersection of two straight lines. Vertical angles are always equal to each other. Example: In the diagram shown, angles AEC and BED are equal because they are vertical angles. For the same reason, angles AED and BEC are equal.

504. When two parallel lines are crossed by a third straight line (called a transversal), then all the acute angles formed are equal, and all of the obtuse angles are equal. Example: In the diagram below, angles 1, 4, 5, and 8 are all equal. Angles 2, 3, 6, and 7 are also equal.

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Triangles 505. Triangles. A triangle is a closed figure with three sides, each side being a line segment. The sum of the angles of a triangle is always 180°. 506. Scalene triangles are triangles with no two sides equal. Scalene triangles also have no two angles equal.

507. Isosceles triangles have two equal sides and two equal angles formed by the equal sides and the unequal side. See the figure below. ab A B C 180° 2(A)

508. Equilateral triangles have all three sides and all three angles equal. Since the sum of the three angles of a triangle is 180°, each angle of an equilateral triangle is 60°. abc A B C 60°

509. A right triangle has one angle equal to a right angle (90°). The sum of the other two angles of a right triangle is, therefore, 90°. The most important relationship in a right triangle is the Pythagorean Theorem. It states that c2 a2 b2, where c is the length of the side opposite the right angle, and a and b are the lengths of the other two sides. Recall that this was discussed in Section 317.

Example: If the two sides of a right triangle adjacent to the right angle are 3 inches and 4 inches respectively, find the length of the side opposite the right angle. Solution:

Use the Pythagorean Theorem, c2 a2 b2, where a 3 and b 4. Then, c 32 42 or c2 9 16 25. Thus c 5.

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Certain sets of numbers will always fit the formula c2 a2 b2. These numbers can always represent the lengths of the sides of a right triangle. For example, a triangle whose sides are 3, 4, and 5 will always be a right triangle. Further examples are 5, 12, and 13; 8, 15, and 17. Any multiples of these numbers also satisfy the formula. For example, 6, 8, and 10; 9, 12, and 15; 10, 24, and 26; 24, 45, and 51, etc.

Properties of Triangles 510. Two triangles are said to be similar (having the same shape) if their corresponding angles are equal. The sides of similar triangles are in the same proportion. The two triangles below are similar because they have the same corresponding angles.

a:d b:e c:f Example: Two triangles both have angles of 30°, 70°, and 80°. If the sides of the triangles are as indicated below, find the length of side x.

Solution: The two triangles are similar because they have the same corresponding angles. The corresponding sides of similar triangles are in proportion, so x : 3 6 : 4. This 6 18 1 x can be rewritten as . Multiplying both sides by 3 gives x , or x 4. 4 4 2 3 511. Two triangles are congruent (identical in shape and size) if any one of the following conditions is met: 1. Each side of the first triangle equals the corresponding side of the second triangle. 2. Two sides of the first triangle equal the corresponding sides of the second triangle, and their included angles are equal. The included angle is formed by the two sides of the triangle. 3. Two angles of the first triangle equal the corresponding angles of the second triangle, and any pair of corresponding sides are equal.

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Example: Triangles ABC and DEF in the diagram below are congruent if any one of the following conditions can be met:

1. The three sides are equal (sss) (sss).

2. Two sides and the included angle are equal (sas) (sas).

3. Two angles and any one side are equal (aas) (aas) or (asa) (asa).

Example: In the equilateral triangle below, line AD is perpendicular (forms a right angle) to side BC. If the length of BD is 5 feet, what is the length of DC ?

Solution: Since the large triangle is an equilateral triangle, each is 60°. Therefore B is 60° and C is 60°. Thus, B C. ADB and ADC are both right angles and are equal. Two angles of each triangle are equal to the corresponding two angles of the other triangle. Side AD is shared by both triangles and side AB side AC. Thus, according to condition 3 in Section 511, the two triangles are congruent. Then BD DC and, since BD is 5 feet, DC is 5 feet. 512. The medians of a triangle are the lines drawn from each vertex to the midpoint of its opposite side. The medians of a triangle cross at a point that divides each median into two parts: one part of one-third the length of the median and the other part of two-thirds the length.

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513. The angle bisectors of a triangle are the lines that divide each angle of the triangle into two equal parts. These lines meet in a point that is the center of a circle inscribed in the triangle.

514. The altitudes of the triangle are lines drawn from the vertices perpendicular to the opposite sides. The lengths of these lines are useful in calculating the area of the triangle since 1 the area of the triangle is (base)(height) and the height is identical to the altitude. 2

515. The perpendicular bisectors of the triangle are the lines that bisect and are perpendicular to each of the three sides. The point where these lines meet is the center of the circumscribed circle.

516.

The sum of any two sides of a triangle is greater than the third side.

Example: If the three sides of a triangle are 4, 2, and x, then what is known about the value of x? Solution: Since the sum of two sides of a triangle is always greater than the third side, then 4 2 x, 4 x 2, and 2 x 4. These three inequalities can be rewritten as 6 x, x 2, and x 2. For x to be greater than 2 and 2, it must be greater than 2. Thus, the values of x are 2 x 6.

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Four-Sided Figures 517.

A parallelogram is a four-sided figure with each pair of opposite sides parallel.

A parallelogram has the following properties: 1. 2. 3. 4.

Each pair of opposite sides are equal. (AD BC, AB DC ) The diagonals bisect each other. ( AF FC, DF FB) The opposite angles are equal. (A C, D B) One diagonal divides the parallelogram into two congruent triangles. Two diagonals divide the parallelogram into two pairs of congruent triangles.

518. A rectangle is a parallelogram in which all the angles are right angles. Since a rectangle is a parallelogram, all of the laws that apply to a parallelogram apply to a rectangle. In addition, the diagonals of a rectangle are equal. AC BD

519. A rhombus is a parallelogram with four equal sides. Since a rhombus is a parallelogram, all of the laws that apply to a parallelogram apply to a rhombus. In addition, the diagonals of a rhombus are perpendicular to each other and bisect the vertex angles. DAC BAC DCA BCA ADB CDB ABD CBD AC is perpendicular to DB

520.

A square is a rectangular rhombus. Thus the square has the following properties:

1. All four sides are equal. (AB BC CD DA) 2. Opposite pairs of sides are parallel. (AD || BC, AB || DC ) 3. Diagonals are equal, are perpendicular to each other, and bisect each other. (AC BD, AC BD, AE EC DE EB)

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4. All the angles are right angles (90°). (A B C D 90°) 5. Diagonals intersect the vertices at 45°. (DAC BAC 45°, and similarly for the other 3 vertices.)

Many-Sided Figures 521. A polygon is a closed plane figure whose sides are straight lines. The sum of the angles in any polygon is equal to 180(n 2)°, where n is the number of sides. Thus, in a polygon of 3 sides (a triangle), the sum of the angles is 180(3 2)° or 180°. 522. A regular polygon is a polygon all of whose sides are equal and all of whose angles are equal. These polygons have special properties: 1. A regular polygon can be inscribed in a circle and can be circumscribed about another circle. For example, a hexagon is inscribed in a circle in the diagram below.

2. Each angle of a polygon is equal to the sum of the angles divided by the number of sides, 180(n 2)° . Thus, a square, which is a regular polygon of 4 sides, has each angle equal to n 180(4 2)° or 90°. 4 523. An important regular polygon is the hexagon. The diagonals of a regular hexagon divide it into 6 equilateral triangles, the sides of which are equal to the sides of the hexagon. If a hexagon is inscribed in a circle, the length of each side is equal to the length of the radius of the circle. (See diagram of hexagon.)

Circles 524. A circle (also see Section 310) is a set of points equidistant from a given point, the center. The distance from the center to the circle is the radius. Any line that connects two points on the circle is a chord. A chord through the center of the circle is a diameter. On the circle below O is the center, line segment OF is a radius, DOE is a diameter, and AC is a chord.

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The length of the diameter of a circle is twice the length of the radius. The circumference (length 22 of the curve) is 2 times the length of the radius. is a constant approximately equal to or 7 3.14. The formula for the circumference of a circle is, C 2r where C circumference and r radius. 525. A tangent to a circle is a line that is perpendicular to a radius and that passes through only one point of the circle. In the diagram AB is a tangent.

526. A central angle is an angle whose sides are two radii of the circle. The vertex of this angle is the center of the circle. The number of degrees in a central angle is equal to the amount of arc length that the radii intercept. As the complete circumference has 360°, any other arc lengths are less than 360°.

Angles AOB, COD, and FOG are all central angles. 527. An inscribed angle of a circle is an angle whose sides are two chords. The vertex of the angle lies on the circumference of the circle. The number of degrees in the inscribed angle is equal to one-half the intercepted arc.

BAC is an inscribed angle.

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528. An angle inscribed in a semicircle is always a right angle. ABC and ADC are inscribed in semicircles AOCB and AOCD, respectively, and are thus right angles. Note: A semicircle is one-half of a circle.

529.

Two tangents to a circle from a point outside of the circle are always equal.

Tangents AB and AD are equal.

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Practice Test 5 Geometry Problems Correct answers and solutions follow each test. 1.

A

B

C

D

E

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1.

In the following diagram, angle 1 is equal to 40°, and angle 2 is equal to 150°. What is the number of degrees in angle 3?

(A) 70° (B) 90° (C) 110° (D) 190° (E) The answer cannot be determined from the given information. 2.

A

B

C

D

E

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2.

In this diagram, AB and CD are both perpendicular to BE. If EC 5, and CD 4, what is the ratio of AB to BE?

(A) (B) (C) (D) (E) 3.

A

B

C

D

E

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3.

In triangle PQR, PR 7.0, and PQ 4.5. Which of the following cannot possibly represent the length of QR? (A) (B) (C) (D) (E)

4.

A

B

C

D

E

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A

B

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2.0 3.0 3.5 4.5 5.0

4. In this diagram, AB AC, and BD CD. Which of the following statements is true?

(A) (B) (C) (D) (E) 5.

1:1 4:3 5:4 5:3 None of these.

5.

BE EC. AD is perpendicular to BC. Triangles BDE and CDE are congruent. Angle ABD equals angle ACD. All of these.

In the following diagram, if BC CD BD 1, and angle ADC is a right angle, what is the perimeter of triangle ABD?

(A) (B) (C) (D) (E)

3 2 2 2 3 3 3 4

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6.

A

B

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E

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6.

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In this diagram, if PQRS is a parallelogram, which of the following can be deduced: I. QT PT RT ST II. QS is perpendicular to PR III. The area of the shaded portion is exactly three times the area of triangle QRT. (A) (B) (C) (D) (E)

7.

A

B

C

D

E

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7.

James lives on the corner of a rectangular field that measures 120 yards by 160 yards. If he wants to walk to the opposite corner, he can either travel along the perimeter of the field or cut directly across in a straight line. How many yards does he save by taking the direct route? (Express to the nearest ten yards.) (A) (B) (C) (D) (E)

8.

A

B

C

D

E

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8.

A

B

C

D

E

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2 (A) 2

9.

A

B

C

D

E

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10.

2 2 2 2 4

How many degrees are there in the angle formed by two adjacent sides of a regular nonagon (nine-sided polygon)? (A) (B) (C) (D) (E)

10.

40 yards 60 yards 80 yards 100 yards 110 yards

In a square, the perimeter is how many times the length of the diagonal?

(B) (C) (D) (E) 9.

I only I and II only II only I and III only I, II, and III

40° 70° 105° 120° 140°

In the diagram below, AB CD. From this we can deduce that: (A) (B) (C) (D) (E)

AB is parallel to CD. AB is perpendicular to BD. AC BD Angle ABD equals angle BDC. Triangle ABD is congruent to triangle ACD.

(Note: Figure is not drawn to scale.)

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11.

A

B

C

D

E

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11.

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If two lines, AB and CD, intersect at a point E, which of the following statements is not true? (A) (B) (C) (D) (E)

12.

A

B

C

D

E

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12.

Angle AEB equals angle CED. Angles AEC and BEC are complementary. Angle CED is a straight angle. Angle AEC equals angle BED. Angle BED plus angle AED equals 180 degrees.

In the following diagram, AC CE and BD DE. Which of these statements is (are) true? I. AB is twice as long as CD. II. AB is parallel to CD. III. Triangle AEB is similar to triangle CED. (A) (B) (C) (D) (E)

13.

A

B

C

D

E

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13.

In triangle ABC, angle A is obtuse, and angle B equals 30°. Which of the following statements best describes angle C? (A) (B) (C) (D) (E)

14.

A

B

C

D

E

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14.

A

B

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E

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15.

Angle C must be less than 60°. Angle C must be less than or equal to 60°. Angle C must be equal to 60°. Angle C must be greater than or equal to 60°. Angle C must be greater than 60°.

In this diagram, ABCD is a parallelogram, and BFDE is a square. If AB 20 and CF 16, what is the perimeter of the parallelogram ABCD? (A) (B) (C) (D) (E)

15.

I only II and III only I and III only I, II, and III None of these.

72 78 86 92 96

The hypotenuse of a right triangle is exactly twice as long as the shorter leg. What is the number of degrees in the smallest angle of the triangle? (A) (B) (C) (D) (E)

30° 45° 60° 90° The answer cannot be determined from the given information.

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16.

A

B

C

D

E

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16.

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The legs of an isosceles triangle are equal to 17 inches each. If the altitude to the base is 8 inches long, how long is the base of the triangle? (A) (B) (C) (D) (E)

17.

A

B

C

D

E

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17.

The perimeter of a right triangle is 18 inches. If the midpoints of the three sides are joined by line segments, they form another triangle. What is the perimeter of this new triangle? (A) (B) (C) (D) (E)

18.

19.

A

B

C

D

E

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A

B

C

D

E

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18.

A

B

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E

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20.

A

B

C

D

E

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21.

45° 60° 75° 90° None of these.

This diagram depicts a rectangle inscribed in a circle. If the measurements of the rectangle are 10 14, what is the area of the circle? (A) (B) (C) (D) (E)

21.

right triangles isosceles triangles similar triangles equilateral triangles equal in area

In the diagram below, ABCDEF is a regular hexagon. How many degrees are there in angle ADC?

(A) (B) (C) (D) (E)

20.

3 inches 6 inches 9 inches 12 inches The answer cannot be determined from the given information.

If the diagonals of a square divide it into four triangles, the triangles cannot be (A) (B) (C) (D) (E)

19.

15 inches 20 inches 24 inches 25 inches 30 inches

74 92 144 196 296

How many degrees are included between the hands of a clock at 5:00? (A) (B) (C) (D) (E)

50° 60° 75° 120° 150°

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22.

A

B

C

D

E

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22.

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ABCD is a square. If the midpoints of the four sides are joined to form a new square, the perimeter of the old square is how many times the perimeter of the new square? (A) (B) (C) (D) (E)

23.

A

B

C

D

E

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23.

A

B

C

D

E

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24.

A

B

C

D

E

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25.

A

B

C

D

E

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26.

A

B

C

D

E

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27.

72 96 120 144 150

AE BE Angle AEB equals angle CED. AE is perpendicular to BD. Triangles AED and AEB are equal in area. Angle BAC equals angle BDC.

City A is 200 miles from City B, and City B is 400 miles from City C. Which of the following best describes the distance between City A and City C? (Note: The cities A, B, C do not all lie on a straight line.) (A) (B) (C) (D) (E)

27.

Angle C is between 0° and 180°. Angle C is between 0° and 90°. Angle C is between 60° and 180°. Angle C is between 60° and 120°. Angle C is between 60° and 90°.

ABCD is a rectangle; the diagonals AC and BD intersect at E. Which of the following statements is not necessarily true? (A) (B) (C) (D) (E)

26.

2 2 2 4

The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. What is the number of degrees in the largest angle? (A) (B) (C) (D) (E)

25.

2

Angles A and B of triangle ABC are both acute angles. Which of the following best describes angle C? (A) (B) (C) (D) (E)

24.

1

It must be greater than zero. It must be greater than 200 miles. It must be less than 600 miles and greater than zero. It must be less than 600 miles and greater than 200. It must be exactly 400 miles.

At 7:30, how many degrees are included between the hands of a clock? (A) (B) (C) (D) (E)

15° 30° 45° 60° 75°

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28.

A

B

C

D

E

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28.

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If a ship is sailing in a northerly direction and then turns to the right until it is sailing in a southwesterly direction, it has gone through a rotation of: (A) (B) (C) (D) (E)

29.

A

B

C

D

E

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29.

x, y, and z are the angles of a triangle. If x 2y, and y z 30°, how many degrees are there in angle x? (A) (B) (C) (D) (E)

30.

A

B

C

D

E

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30.

A

B

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D

E

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31.

33.

A

B

C

D

E

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A

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E

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32.

1:2 1 : 2 1:1 2 :1 2:1

How many degrees are there between two adjacent sides of a regular ten-sided figure? (A) (B) (C) (D) (E)

33.

1 2 180° 4 7 5 8 2 4 360° 2 3 180° 2 6

What is the ratio of the diagonal of a square to the hypotenuse of the isosceles right triangle having the same area? (A) (B) (C) (D) (E)

32.

22.5° 37.5° 52.5° 90.0° 105.0°

In the diagram shown, AB is parallel to CD. Which of the following statements is not necessarily true? (A) (B) (C) (D) (E)

31.

45° 90° 135° 180° 225°

36° 72° 120° 144° 154°

Which of the following sets of numbers cannot represent the lengths of the sides of a right triangle? (A) (B) (C) (D) (E)

5, 12, 13 4.2, 5.6, 7.0 9, 28, 35 16, 30, 34 7.5, 18, 19.5

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34.

35.

A

B

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D

E

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A

B

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E

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34.

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How many degrees are there in the angle that is its own supplement? (A) (B) (C) (D) (E)

35.

30° 45° 60° 90° 180°

If a central angle of 45° intersects an arc 6 inches long on the circumference of a circle, what is the radius of the circle? 4 inches (A) 2 8 inches (B) 4 (C) 6 inches (D) 24 inches (E) 48 inches

36.

A

B

C

D

E

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36.

What is the length of the line segment connecting the two most distant vertices of a 1-inch cube? (A) (B) (C) (D) (E)

37.

38.

A

B

C

D

E

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37.

Through how many degrees does the hour hand of a clock move in 70 minutes? (A) (B) (C) (D) (E)

38.

1 inch 2 inches 3 inches 5 inches 6 inches

35° 60° 80° 90° 120°

In the diagram pictured below, BA is tangent to circle O at point A. CD is perpendicular to OA at C. Which of the following statements is (are) true? I. Triangles ODC and OBA are similar. II. OA : DC OB : AB III. AB is twice as long as CD. (A) (B) (C) (D) (E)

39.

A

B

C

D

E

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39.

I only III only I and II only II and III only None of the above combinations.

The three angles of triangle ABC are in the ratio 1 : 2 : 6. How many degrees are in the largest angle? (A) (B) (C) (D) (E)

45° 90° 120° 135° 160°

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40.

A

B

C

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E

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40.

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In this diagram, AB AC, angle A 40°, and BD is perpendicular to AC at D. How many degrees are there in angle DBC ? (A) (B) (C) (D) (E)

41.

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D

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41.

If the line AB intersects the line CD at point E, which of the following pairs of angles need not be equal? (A) (B) (C) (D) (E)

42.

43.

44.

45.

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B

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E

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42.

39 square inches 52 square inches 60 square inches 65 square inches The answer cannot be determined from the given information.

If each side of an equilateral triangle is 2 inches long, what is the triangle’s altitude? (A) (B) (C) (D) (E)

45.

similar congruent equilateral equal in area None of these.

What is the area of a triangle whose sides are 10 inches, 13 inches, and 13 inches? (A) (B) (C) (D) (E)

44.

AEB and CED AEC and BED AED and CEA BEC and DEA DEC and BEA

All right isosceles triangles must be (A) (B) (C) (D) (E)

43.

20° 40° 50° 70° None of these.

1 inch 2 inches 3 inches 2 inches 5 inches

In the parallelogram ABCD, diagonals AC and BD intersect at E. Which of the following must be true? (A) (B) (C) (D) (E)

AED BEC AE EC BDC DBA Two of the above must be true. All three of the statements must be true.

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45.

A

B

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E

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46. If ABCD is a square, and diagonals AC and BD intersect at point E, how many isosceles

right triangles are there in the figure? (A) (B) (C) (D) (E)

47.

48.

A

B

C

D

E

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4 5 6 7 8

47. How many degrees are there in each angle of a regular hexagon?

(A) (B) (C) (D) (E)

60° 90° 108° 120° 144°

48. The radius of a circle is 1 inch. If an equilateral triangle is inscribed in the circle, what

will be the length of one of the triangle’s sides? (A) 1 inch 2 (B) inches 2 inches (C) 2 3 (D) inches 2 3 inches (E)

49.

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B

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E

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49. If the angles of a triangle are in the ratio 2 : 3 : 4, how many degrees are there in the

largest angle? (A) (B) (C) (D) (E)

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B

C

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20° 40° 60° 80° 120°

50. Which of the following combinations may represent the lengths of the sides of a right

triangle? (A) (B) (C) (D) (E)

4, 6, 8 12, 16, 20 7, 17, 23 9, 20, 27 None of these.

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C B A E C D C D E D B D A

14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.

E A E C D B A E B A D C D

27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38.

C E E D B D C D A C A C

39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.

C A C A C C E E D E D B


Choice C is correct. In the problem it is given that 1 40° and 2 150°. The diagram below makes it apparent that: (1) 1 4 and 3 5 (vertical angles); (2) 6 2 180° (straight angle); (3) 4 5 6 180° (sum of angles in a triangle). To solve the problem, 3 must be related through the above information to the known quantities in 1 and 2. Proceed as follows: 3 5, but 5 180° 4 6. 4 1 40° and 6 180° 2 180° 150° 30°. Therefore, 3 180° 40° 30° 110°. (501, 503, 505)

2.

Choice B is correct. Since CD is perpendicular to DE, CDE is a right triangle, and using the Pythagorean Theorem yields DE 3. Thus, the ratio of CD to DE is 4 : 3. But triangle ABE is similar to triangle CDE. Therefore, AB : BE CD : DE 4 : 3. (509, 510)

3.

Choice A is correct. In a triangle, it is impossible for one side to be longer than the sum of the other two (a straight line is the shortest distance between two points). Thus 2.0, 4.5, and 7.0 cannot be three sides of a triangle. (516)

4.

Choice E is correct. AB AC, BD CD, and AD equal to itself is sufficient information (three sides) to prove triangles ABD and ACD congruent. Also, since AB AC, AE AE, and BAE CAE (by the previous congruence), triangles ABE and ACE are congruent. Since BD CD, ED ED, and angle BDE equals angle CDE (by initial congruence), triangles BDE and CDE are congruent. Through congruence of triangle ABE and triangle ACE, angles BEA and CEA are equal, and their sum is a straight angle (180°). They must both be right angles. Thus, from the given information, we can deduce all the properties given as choices. (511)

5.

Choice C is correct. The perimeter of triangle ABD is AB BD AD. The length of BD is 1. Since BC CD BD, triangle BCD is an equilateral triangle. Therefore, angle C 60° and angle BDC 60°. Angle A angle C 90° (the sum of two acute angles in a right

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triangle is 90°) and angle BDC angle BDA 90° (these two angles form a right angle). Since angle C and angle BDC both equal 60°, angle A angle BDA 30°. Now two angles of triangle ADB are equal. Therefore, triangle ADB is an isosceles triangle with side BD side AB. Since BD 1, then AB 1. AD is a leg of the right triangle, with side CD 1 and hypotenuse AC 2. (AC AB BC 1 1.) Using the relationship c2 a2 b2 gives us the length of AD as 3 . Thus the perimeter is 1 1 3 or 2 3. (505, 507, 509) 6.

Choice D is correct. (I) must be true, since the diagonals of a parallelogram bisect each other, so QT ST, and PT RT. Thus, since the sums of equals are equal, QT PT RT ST. (II) is not necessarily true and, in fact, can be true only if the parallelogram is also a rhombus (all four sides equal). (III) is true, since the four small triangles each have the same area. The shaded portion contains three such triangles. This can be seen by noting that the altitudes from point P to the bases of triangles PQT and PTS are identical. We have already seen from part (I) that these bases (QT and TS) are also equal. Therefore, only I and III can be deduced from the given information. (514, 517)

7.


The diagonal path divides the rectangular field into two right triangles. The Pythagorean Theorem gives the length of the diagonal as 200 yards. If James takes the route around the perimeter, he will travel 120 160, or 280 yards. Thus, the shorter route saves him 80 yards. (509, 518)

8.

Choice D is correct. Let one side of a square be s. Then the perimeter must be 4s. The diagonal of a square with side s is equal to s 2. Dividing the perimeter by the diagonal produces 2 2 . The perimeter is 2 2 times the diagonal. (509, 520)

9.

Choice E is correct. The sum of the angles of any polygon is equal to 180° (n 2), where n is the number of sides. Thus the total number of degrees in a nonagon 180°(9 2) 1,260° 1,260° 180° 7 1,260°. The number of degrees in each angle is 140°. n 9 (521, 522)

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10.

Choice D is correct. Since chord AB equals chord CD, it must be true that arc AB equals arc CD. By adding arc AC to arc CD and to arc AB it is apparent that arc ACD is equal to arc CAB. These arcs are intersected by inscribed angles ABD and BDC. Therefore, the two inscribed angles must be equal. If we redraw the figure as shown below, the falseness of statements (A), (B), (C), and (E) becomes readily apparent. (527)

11.

Choice B is correct. AEC BEC AEB, a straight angle (180°). Thus, angles AEC and BEC are supplementary. (Complementary means that the two angles add up to a right angle, or 90°.) (501, 502)

12.

Choice D is correct. Since AC CE and BD DE, triangles AEB and CED are similar, and AE is twice as long as CE, since by proportionality, AB : CD AE : CE 2 : 1. From the similarity it is found that angle ABE equals angle CDE, and, therefore, that AB is parallel to CD. Thus, all three statements are true. (504, 510)

13.

Choice A is correct. Angle A must be greater than 90°; angle B equals 30°. Thus, the sum of angles A and B must be greater than 120°. Since the sum of the three angles A, B, and C must be 180°, angle C must be less than 60°. (It cannot equal 60°, because then angle A would be a right angle instead of an obtuse angle.) (501, 505)

14.

Choice E is correct. CDF is a right triangle with one side of 16 and a hypotenuse of 20. Thus, the third side, DF, equals 12. Since BFDE is a square, BF and ED are also equal to 12. Thus, BC 12 16 28, and CD 20. ABCD is a parallelogram, so AB CD, AD BC. The perimeter is 28 20 28 20 96. (509, 517, 520)

15.

Choice A is correct. Either recognize immediately that the sides of a 30° 60° 90° triangle are in the proportion 1 : 3 : 2, and the problem is solved, or construct an isosceles triangle by placing two of the right triangles so that the unknown sides touch (see diagram). This isosceles triangle is equilateral with angles of 60°. Therefore, the smallest angle in the right triangle is equal to angle BAC, or 30°. (509)

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16.

Choice E is correct. The altitude to the base of an isosceles triangle divides it into two congruent right triangles, each with one leg of 8 inches, and a hypotenuse of 17 inches. By the Pythagorean Theorem, the third side of each right triangle must be 15 inches long. The base of the isosceles triangle is the sum of two such sides, totaling 30 inches. (507, 509, 514)

17.

Choice C is correct. Call the triangle ABC, and the triangle of midpoints PQR, where P is the midpoint of BC, Q is the midpoint of AC, and R is the midpoint of AB. Then, PQ is 1 1 equal to half the length of AB, QR BC, and PR AC. This has nothing to do with the 2 2 fact that ABC is a right triangle. Thus, the perimeter of the small triangle is equal to 1 PQ QR PR (AB BC AC). The new perimeter is half the old perimeter, 2 or 9 inches. (509, 510, 512)

18.

Choice D is correct. The diagonals of the square form four right triangles, each of which is isosceles because each has two 45° angles. The triangles are all identical in shape and size, so they all are similar and have the same area. The only choice left is equilateral, which cannot be true, since then the sum of the angles at the intersection of the diagonals must be 360°. The sum of four 60° angles would be only 240°. (520)

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19.

Choice B is correct. First, draw in the lines CF and BE. These intersect AD at its midpoint (also the midpoint of CF and BE) and divide the hexagon into six equilateral triangles. Since ADC is an angle of one of these equilateral triangles, it must be equal to 60°. (Another way to do this problem is to calculate the number of degrees in one angle of a regular hexagon and divide this by 2.) (508, 523)

20.

Choice A is correct. The diagonal of an inscribed rectangle is equal to the diameter of the circle. To find this length, use the Pythagorean Theorem on one of the two triangles formed by two of the sides of the rectangle and the diagonal. Thus, the square of the diagonal is equal to 102 142 100 196 296. The area of the circle is equal to times the square of the radius. The square of the radius of the circle is one-fourth of the diameter squared (since d 2r, d 2 4r 2 ) or 74. Thus, the area is 74. (509, 518, 524)

21.

Choice E is correct. Each number on a clock (or hour marking) represents an angle of 30°, as 360° divided by 12 is 30° (a convenient fact to remember for other clock problems). Since the hands of the clock are on the 12 and the 5, there are five hour units between the hands; 5 30° 150°. (501, 526)

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22.


Let S represent the side of the large square. Then the perimeter is 4S. Let s represent the side of the smaller square. Then the perimeter is 4s. Line NQ is the diagonal of the smaller square, so the length of NQ is 2s. (The diagonal of a square is 2 times the side.) Now, NQ is equal to DC, or S, which is the side of the larger square. So now S 2 s. The perimeter of the large square equals 4S 42 s 2 (4s) 2 perimeter of the small square. (520) 23.

Choice A is correct. Angles A and B are both greater than 0 degrees and less than 90 degrees, so their sum is between 0 degrees and 180 degrees. Then angle C must be between 0 and 180 degrees. (501, 505)

24.

Choice D is correct. Let the four angles be x, 2x, 3x, and 4x. The sum, 10x, must equal 360°. Thus, x 36°, and the largest angle, 4x, is 144°. (505)

25.

Choice C is correct. The diagonals of a rectangle are perpendicular only when the rectangle is a square. AE is part of the diagonal AC, so AE will not necessarily be perpendicular to BD. (518)

26.


Draw the three cities as the vertices of a triangle. The length of side CB is 400 miles, the length of side AB is 200 miles, and x, the length of side AC, is unknown. The sum of any two sides of a triangle is greater than the third side, or in algebraic terms: 400 200 x, 400 x 200 and 200 x 400. These simplify to 600 x, x 200, and x 200. For x to be greater than 200 and 200, it must be greater than 200. Thus, the values of x are 200 x 600. (506, 516) 27.

Choice C is correct. At 7:30, the hour hand is halfway between the 7 and the 8, and the minute hand is on the 6. Thus, there are one and one-half “hour units,” each equal to 30°, so the whole angle is 45°. (501, 526)

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28.

Choice E is correct. If a ship is facing north, a right turn of 90° will face it eastward. Another 90° turn will face it south, and an additional 45° turn will bring it to southwest. Thus, the total rotation is 90° 90° 45° 225°. (501)

29.

Choice E is correct. Since y z 30° and x 2y, then x 2(z 30°) 2z 60°. Thus, x y z equals (2z 60°) (z 30°) z 4z 90°. This must equal 180° (the sum 1° of the angles of a triangle). So 4z 90° 180°, and the solution is z 22; 2 x 2z 60° 45° 60° 105°. (505)

30.

Choice D is correct. Since AB is parallel to CD, angle 2 angle 6, and angle 3 angle 7 180°. If angle 2 angle 3 equals 180°, then angle 2 angle 7 angle 6. However, since there is no evidence that angles 6 and 7 are equal, angle 2 angle 3 does not necessarily equal 180°. Therefore, the answer is (D). (504)

31.

Choice B is correct. Call the side of the square, s. Then, the diagonal of the square is 2s 1 and the area is s2. The area of an isosceles right triangle with leg r is r 2. Now, the area 2 1 of the triangle is equal to the area of the square so s2 r 2. Solving for r gives r 2 2 r2 Substituting r 2 s. The hypotenuse of the triangle is r. s, the hypotenuse is 2 2 2 4s 2s 2s 2 2s. Therefore, the ratio of the diagonal to the hypotenuse is 2s 2 2 s : 2s is or , multiply by which has a value of 1. 2s : 2s. Since 2 2s 2 2 2 2 2 1 Thus or 1 : 2, which is the final result. 2 2 22 2 (507, 509, 520)

32.

Choice D is correct. The formula for the number of degrees in the angles of a polygon is 180(n 2), where n is the number of sides. For a ten-sided figure this is 10(180°) 360° (1800 360)° 1440°. Since the ten angles are equal, they must each equal 144°. (521, 522)

33.

Choice C is correct. If three numbers represent the lengths of the sides of a right triangle, they must satisfy the Pythagorean Theorem: The squares of the smaller two must equal the square of the largest one. This condition is met in all the sets given except the set 9,28,35. There, 92 282 81 784 865, but 352 1,225. (509)

34.

Choice D is correct. Let the angle be x. Since x is its own supplement, then x x 180°, or, since 2x 180°, x 90°. (502)

35.

Choice A is correct. The length of the arc intersected by a central angle of a circle is proportional to the number of degrees in the angle. Thus, if a 45° angle cuts off a 6-inch arc, a 360° angle intersects an arc eight times as long, or 48 inches. This is equal to the circle’s circumference, or 2 times the radius. Thus, to obtain the radius, divide 48 inches 24 by 2. 48 inches 2 inches. (524, 526)

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36.

Choice C is correct. Refer to the diagram pictured below. Calculate the distance from vertex 1 to vertex 2. This is simply the diagonal of a 1-inch square and equal to 2 inches. Now, vertices 1, 2, and 3 form a right triangle, with legs of 1 and 2 . By the Pythagorean Theorem, the hypotenuse is 3. This is the distance from vertex 1 to vertex 3, the two most distant vertices. (509, 520)

37.

Choice A is correct. In one hour, the hour hand of a clock moves through an angle of 30° 7 (one “hour unit”). 70 minutes equals hours, so during that time the hour hand will move 6 7 (501, 526) through 30°, or 35°. 6

38.

Choice C is correct. In order to be similar, two triangles must have corresponding angles equal. This is true of triangles ODC and OBA, since angle O equals itself, and angles OCD and OAB are both right angles. (The third angles of these triangles must be equal, as the sum of the angles of a triangle is always 180°.) Since the triangles are similar, OD : DC OB : AB. But, OD and OA are radii of the same circle and are equal. Therefore, substitute OA for OD in the above proportion. Hence, OA : DC OB : AB. There is, however, no information given on the relative sizes of any of the line segments, so statement III may or may not be true. (509, 510, 524)

39.

Choice C is correct. Let the three angles equal x, 2x, and 6x. Then, x 2x 6x 9x 180°. Therefore, x 20° and 6x 120°. (505)

40.

Choice A is correct. Since AB AC, angle ABC must equal angle ACB. (Base angles of an isosceles triangle are equal). As the sum of angles BAC, ABC, and ACB is 180°, and angle BAC equals 40°, angle ABC and angle ACB must each equal 70°. Now, DBC is a right triangle, with angle BDC 90° and angle DCB 70°. (The three angles must add up to 180°.) Angle DBC must equal 20°. (507, 514)

41.


AEB and CED are both straight angles, and are equal; similarly, DEC and BEA are both straight angles. AEC and BED are vertical angles, as are BEC and DEA, and are equal. AED and CEA are supplementary and need not be equal. (501, 502, 503) 42.

Choice A is correct. All right isosceles triangles have angles of 45°, 45°, and 90°. Since all triangles with the same angles are similar, all right isosceles triangles are similar. (507, 509, 510)

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43.


As the diagram shows, the altitude to the base of the isosceles triangle divides it into two congruent right triangles, each with 51213 sides. Thus, the base is 10, height is 12 and 1 (505, 507, 509) the area is (10)(12) 60. 2 44.

Choice C is correct. The altitude to any side divides the triangle into two congruent 30°– 60°–90° right triangles, each with a hypotenuse of 2 inches and a leg of 1 inch. The other leg equals the altitude. By the Pythagorean Theorem the altitude is equal to 3 inches. (The sides of a 30°60°90° right triangle are always in the proportion 1 : 3 : 2.) (509, 514)

45.


As the diagram illustrates, angles AED and BEC are vertical and, therefore, equal. AE EC, because the diagonals of a parallelogram bisect each other. Angles BDC and DBA are equal because they are alternate interior angles of parallel lines (AB CD). (503, 517) 46.

Choice E is correct. There are eight isosceles right triangles: ABE, BCE, CDE, ADE, ABC, BCD, CDA, and ABD. (520)

47.

Choice D is correct. Recall that a regular hexagon may be broken up into six equilateral triangles.

Since the angles of each triangle are 60°, and two of these angles make up each angle of the hexagon, an angle of the hexagon must be 120°. (523)

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48.


Since the radius equals 1, AD, the diameter, must be 2. Now, since AD is a diameter, ACD must be a right triangle, because an angle inscribed in a semicircle is a right angle. Thus, because DAC 30°, it must be a 30°60°90° right triangle. The sides will be in the proportion 1 : 3 : 2. As AD : AC 2 : 3, so AC, one of the sides of the equilateral triangle, must be 3 inches long. (508, 524) 49.

Choice D is correct. Let the angles be 2x, 3x, 4x. Their sum, 9x 180° and x 20°. Thus, the largest angle, 4x, is 80°. (505)

50.

Choice B is correct. The sides of a right triangle must obey the Pythagorean Theorem. The only group of choices that does so is the second: 12, 16, and 20 are in the 3 : 4 : 5 ratio, and the relationship 122 162 202 is satisfied. (509)

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Miscellaneous Problems Including Averages, Series, Properties of Integers, Approximations, Combinations, Probability, the Absolute Value Sign, and Functions Averages, Medians, and Modes 601. Averages. The average of n numbers is merely their sum, divided by n. Example: Find the average of: 20, 0, 80, and 12. Solution: The average is the sum divided by the number of entries, or: 20 0 80 12 112 28 4 4 A quick way of obtaining an average of a set of numbers that are close together is the following: STEP 1. Choose any number that will approximately equal the average. STEP 2. Subtract this approximate average from each of the numbers (this sum will give some positive and negative results). Add the results. STEP 3. Divide this sum by the number of entries. STEP 4. Add the result of Step 3 to the approximate average chosen in Step 1. This will be the true average. Example: Find the average of 92, 93, 93, 96 and 97. Solution: Choose 95 as an approximate average. Subtracting 95 from 92, 93, 93, 96, and 97 gives 3, 2, 2, 1, and 2. The sum is 4. Divide 4 by 5 (the number of entries) to obtain 0.8. Add 0.8 to the original approximation of 95 to get the true average, 95 0.8 or 94.2.

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601a. Medians. The median of a set of numbers is that number which is in the middle of all the numbers. Example: Find the median of 20, 0, 80, 12, and 30. Solution: Arrange the numbers in increasing order: 0 12 20 30 80 The middle number is 20, so 20 is the median. Note: If there is an even number of items, such as 0 12 20 24 30 80 there is no middle number. So in this case we take the average of the two middle numbers, 20 and 24, to get 22, which is the median. If there are numbers like 20 and 22, the median would be 21 ( just the average of 20 and 22). 601b.

Modes. The mode of a set of numbers is the number that occurs most frequently.

If we have numbers 0, 12, 20, 30, and 80 there is no mode, since no one number appears with the greatest frequency. But consider this: Example: Find the mode of 0, 12, 12, 20, 30, 80. Solution: 12 appears most frequently, so it is the mode. Example: Find the mode of 0, 12, 12, 20, 30, 30, 80. Solution: Here both 12 and 30 are modes.

Series 602. Number series or sequences are progressions of numbers arranged according to some design. By recognizing the type of series from the first four terms, it is possible to know all the terms in the series. Following are given a few different types of number series that appear frequently. 1. Arithmetic progressions are very common. In an arithmetic progression, each term exceeds the previous one by some fixed number. Example: In the series 3, 5, 7, 9, . . . find the next term. Solution: Each term in the series is 2 more than the preceding one, so the next term is 9 2 or 11. If the difference in successive terms is negative, then the series decreases. Example: Find the next term: 100, 93, 86, 79 . . . . Solution: Each term is 7 less than the previous one, so the next term is 72.

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2. In a geometric progression each term equals the previous term multiplied by a fixed number. Example: What is the term of the series 2, 6, 18, 54 . . . ? Solution: Each term is 3 times the previous term, so the fifth term is 3 times 54 or 162. If the multiplying factor is negative, the series will alternate between positive and negative terms. Example: Find the next term of 2, 4, 8, 16 . . . Solution: Each term is 2 times the previous term, so the next term is 32. Example: Find the next term in the series 64, 32, 16, 8 . . . 1 Solution: Each term is times the previous term, so the next term is 4. 2 3. In mixed step progression the successive terms can be found by repeating a pattern of add 2, add 3, add 2, add 3; or a pattern of add 1, multiply by 5, add 1, multiply 5, etc. The series is the result of a combination of operations. Example: Find the next term in the series 1, 3, 9, 11, 33, 35 . . . Solution: The pattern of successive terms is add 2, multiply by 3, add 2, multiply by 3, etc. The next step is to multiply 35 by 3 to get 105. Example: Find the next term in the series 4, 16, 8, 32, 16 . . . Solution: Here, the pattern is to multiply by 4, divide by 2, multiply by 4, divide by 2, etc. Thus, the next term is 16 times 4 or 64. 4. If no obvious solution presents itself, it may be helpful to calculate the difference between each term and the preceding one. Then if it is possible to determine the next increment (the difference between successive terms), add it to the last term to obtain the term in question. Often the series of increments is a simpler series than the series of original terms. Example: Find the next term in the series 3, 9, 19, 33, 51 . . . Solution: Write out the series of increments: 6, 10, 14, 18 . . . (each term is the difference between two terms of the original series). This series is an arithmetic progression whose next term is 22. Adding 22 to the term 51 from the original series produces the next term, 73. 5. If none of the above methods is effective, the series may be a combination of two or three different series. In this case, make a series out of every other term or out of every third term and see whether these terms form a series that can be recognized. Example: Find the next term in the series 1, 4, 4, 8, 16, 12, 64, 16 . . . Solution: Divide this series into two series by taking out every other term, yielding: 1, 4, 16, 64 . . . and 4, 8, 12, 16 . . . These series are easy to recognize as a geometric and arithmetic series, but the first series has the needed term. The next term in this series is 4 times 64 or 256.

Properties of Integers 603. Even-Odd. These are problems that deal with even and odd numbers. An even number is divisible by 2, and an odd number is not divisible by 2. All even numbers end in the digits 0, 2, 4, 6, or 8; odd numbers end in the digits 1, 3, 5, 7, or 9. For example, the numbers 358, 90, 18, 9,874, and 46 are even numbers. The numbers 67, 871, 475, and 89 are odd numbers. It is important to remember the following facts:

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604. The sum of two even numbers is even, and the sum of two odd numbers is even, but the sum of an odd number and an even number is odd. For example, 4 8 12, 5 3 8, and 7 2 9. Example: If m is any integer, is the number 6m 3 an even or odd number? Solution: 6m is even since 6 is a multiple of 2. 3 is odd. Therefore 6m 3 is odd since even odd odd. 605. The product of two odd numbers is odd, but the product of an even number and any other number is an even number. For example, 3 5 15 (odd); 4 5 20 (even); 4 6 24 (even). Example: If m is any integer, is the product (2m 3)(4m 1) even or odd? Solution: Since 2m is even and 3 is odd, 2m 3 is odd. Likewise, since 4m is even and 1 is odd, 4m 1 is odd. Thus (2m 3)(4m 1) is (odd odd) which is odd. 606. Even numbers are expressed in the form 2k where k may be any integer. Odd numbers are expressed in the form of 2k 1 or 2k 1 where k may be any integer. For example, if k 17, then 2k 34 and 2k 1 35. If k 6, then we have 2k 12 and 2k 1 13. Example: Prove that the product of two odd numbers is odd. Solution: Let one of the odd numbers be represented as 2x 1. Let the other number be represented as 2y 1. Now multiply (2x 1)(2y 1). We get: 4xy 2x 2y 1. Since 4xy 2x 2y is even because it is a multiple of 2, that quantity is even. Since 1 is odd, we have 4xy 2x 2y 1 is odd, since even odd odd. 607. Divisibility. If an integer P is divided by an integer Q, and an integer is obtained as the quotient, then P is said to be divisible by Q. In other words, if P can be expressed as an integral multiple of Q, then P is said to be divisible by Q. For example, dividing 51 by 17 gives 3, an 2 integer. 51 is divisible by 17, or 51 equals 17 times 3. On the other hand, dividing 8 by 3 gives 2, 3 which is not an integer. 8 is not divisible by 3, and there is no way to express 8 as an integral multiple of 3. There are various tests to see whether an integer is divisible by certain numbers. These tests are listed below: 1.

Any integer is divisible by 2 if the last digit of the number is a 0, 2, 4, 6, or 8. Example: The numbers 98, 6,534, 70, and 32 are divisible by 2 because they end in 8, 4, 0, and 2, respectively.

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Any integer is divisible by 3 if the sum of its digits is divisible by 3. Example: Is the number 34,237,023 divisible by 3? Solution: Add the digits of the number. 3 4 2 3 7 0 2 3 24. Now, 24 is divisible by 3(24 3 8) so the number 34,237,023 is also divisible by 3.

3. Any integer is divisible by 4 if the last two digits of the number make a number that is divisible by 4. Example: Which of the following numbers is divisible by 4? 3,456, 6,787,612, 67,408, 7,877, 345, 98. Solution: Look at the last two digits of the numbers, 56, 12, 08, 77, 45, 98. Only 56, 12, and 08 are divisible by 4, so only the numbers, 3,456, 6,787,612, and 67,408 are divisible by 4. 4.

An integer is divisible by 5 if the last digit is either a 0 or a 5. Example: The numbers 780, 675, 9,000, and 15 are divisible by 5, while the numbers 786, 5,509, and 87 are not divisible by 5.

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5.

Any integer is divisible by 6 if it passes the divisibility tests for both 2 and 3. Example: Is the number 12,414 divisible by 6? Solution: Test whether 12,414 is divisible by 2 and 3. The last digit is a 4, so it is divisible by 2. Adding the digits yields 1 2 4 1 4 12. 12 is divisible by 3 so the number 12,414 is divisible by 3. Since it is divisible by both 2 and 3, it is divisible by 6.

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Any integer is divisible by 8 if the last three digits are divisible by 8. (Since 1,000 is divisible by 8, you can ignore all multiples of 1,000.) Example: Is the number 342,169,424 divisible by 8? Solution: 424 8 53, so 342,169,424 is divisible by 8.

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Any integer is divisible by 9 if the sum of its digits is divisible by 9. Example: Is the number 243,091,863 divisible by 9? Solution: Adding the digits yields 2 4 3 0 9 1 8 6 3 36. 36 is divisible by 9, so the number 243,091,863 is divisible by 9.

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Any integer is divisible by 10 if the last digit is a 0. Example: The numbers 60, 8,900, 5,640, and 34,000 are all divisible by 10 because the last digit in each is a 0.

Note that if a number P is divisible by a number Q, then P is also divisible by all the factors of Q. For example, 60 is divisible by 12, so 60 is also divisible by 2, 3, 4, and 6, which are all factors of 12.

608. Prime numbers. A prime number is one that is divisible only by 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37. . . . Note that the number 1 is not considered a prime number. To determine if a number is prime, follow these steps: STEP 1. Determine a very rough approximate square root of the number. Remember that the square root of a number is that number which when multiplied by itself gives the original number. For example, the square root of 25 is 5 because 5 5 25. STEP 2. Divide the number by all of the primes that are less than the approximate square root. If the number is not divisible by any of these primes, then it is prime. If it is divisible by one of the primes, then it is not prime. Example: Is the number 97 prime? Solution: An approximate square root of 97 is 10. All of the primes less than 10 are 2, 3, 5, and 7. Divide 97 by 2, 3, 5, and 7. No integer results, so 97 is prime. Example: Is the number 161 prime? Solution: An approximate square root of 161 is 13. The primes less than 13 are 2, 3, 5, 7, and 11. Divide 161 by 2, 3, 5, 7, and 11. 161 is divisible by 7 (161 7 23), so 161 is not prime.

Approximations 609. Rounding off. A number expressed to a certain number of places is rounded off when it is approximated as a number with fewer places of accuracy. For example, the number 8.987 is expressed more accurately than the number rounded off to 8.99. To round off to n places, look at the digit that is to the right of the nth digit. (The nth digit is found by counting n places to the right of the decimal point.) If this digit is less than 5, eliminate all of the digits to the right

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of the nth digit. If the digit to the right of the nth digit is 5 or more, then add 1 to the nth digit and eliminate all of the digits to the right of the nth digit. Example: Round off 8.73 to the nearest tenth. Solution: The digit to the right of the 7 (.7 is seven tenths) is 3. Since this is less than 5, eliminate it, and the rounded off answer is 8.7. Example: Round off 986 to the nearest tens’ place. Solution: The number to the right of the tens’ place is 6. Since this is 5 or more add 1 to the 8 and replace the 6 with a 0 to get 990. 610. Approximating sums. When adding a given set of numbers and when the answer must have a given number of places of accuracy, follow the steps below. STEP 1. Round off each addend (number being added) to one more place than the number of places the answer is to have. STEP 2. Add the rounded addends. STEP 3. Round off the sum to the desired number of places of accuracy. Example: What is the sum of 12.0775, 1.20163, and 121.303 correct to the nearest hundredth? Solution: Round off the three numbers to the nearest thousandth (one more place than the accuracy of the sum): 12.078, 1.202, and 121.303. The sum of these is 134.583. Rounded off to the nearest hundredth, this is 134.58. 611. Approximating products. To multiply certain numbers and have an answer to the desired number of places of accuracy, follow the steps below. STEP 1. Round off the numbers being multiplied to the number of places of accuracy desired in the answer. STEP 2. Multiply the rounded off factors (numbers being multiplied). STEP 3. Round off the product to the desired number of places. Example: Find the product of 3,316 and 1,432 to three places. Solution: First, round off 3,316 to 3 places, to obtain 3,320. Round off 1,432 to 3 places to give 1,430. The product of these two numbers is 4,747,600. Rounded off to 3 places this is 4,750,000. 612. Approximating square roots. The square root of a number is that number which, when multiplied by itself, gives the original number. For example, 6 is the square root of 36. Often on tests a number with different choices for the square root is given. Follow this procedure to determine which is the best choice. STEP 1. Square all of the choices given. STEP 2. Select the closest choice that is too large and the closest choice that is too small (assuming that no choice is the exact square root). Find the average of these two choices (not of their squares). STEP 3. Square this average; if the square is greater than the original number, choose the lower of the two choices; if its square is lower than the original number, choose the higher. Example: Which of the following is closest to the square root of 86: 9.0, 9.2, 9.4, 9.6, or 9.8? Solution: The squares of the five numbers are: 81, 84.64, 88.36, 92.16, and 96.04, respectively. (Actually it was not necessary to calculate the last two, since they are greater than the third square, which is already greater than 86.) The two closest choices are 9.2 and 9.4; their average is 9.3. The square of 9.3 is 86.49. Therefore, 9.3 is greater than the square root of 86. So, the square root must be closer to 9.2 than to 9.4.

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Combinations 613. Suppose that a job has 2 different parts. There are m different ways of doing the first part, and there are n different ways of doing the second part. The problem is to find the number of ways of doing the entire job. For each way of doing the first part of the job, there are n ways of doing the second part. Since there are m ways of doing the first part, the total number of ways of doing the entire job is m n. The formula that can be used is Number of ways m n For any problem that involves 2 actions or 2 objects, each with a number of choices, and asks for the number of combinations, the formula can be used. For example: A man wants a sandwich and a drink for lunch. If a restaurant has 4 choices of sandwiches and 3 choices of drinks, how many different ways can he order his lunch? Since there are 4 choices of sandwiches and 3 choices of drinks, using the formula Number of ways 4(3) 12 Therefore, the man can order his lunch 12 different ways. If we have objects a, b, c, d, and want to arrange them two at a time—that is, like ab, bc, cd, etc.—we have four combinations taken two at a time. This is denoted as 4C2. The rule is that (4)(3) C . In general, n combinations taken r at a time is represented by the formula: 4 2 (2)(1) (n)(n 1)(n 2) … (n r 1) C n r (r)(r 1)(r 2) … (1) 3 2 8 7 6 Examples: 3C2 ; 8C3 2 1 3 2 1 Suppose there are two groups, each with a certain number of members. It is known that some members of one group also belong to the other group. The problem is to find how many members there are in the 2 groups altogether. To find the numbers of members altogether, use the following formula: Total number of members Number of members in group I Number of members in group II Number of members common to both groups For example: In one class, 18 students received A’s for English and 10 students received A’s in math. If 5 students received A’s in both English and math, how many students received at least one A? In this case, let the students who received A’s in English be in group I and let those who received A’s in math be in group II. Using the formula: Number of students who received at least one A Number in group I Number in group II Number in both 18 10 5 23 Therefore, there are 23 students who received at least one A. In combination problems such as these, the problems do not always ask for the total number. They may ask for any of the four numbers in the formula while the other three are given. In any case, to solve the problems, use the formula.

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Probability 614. The probability that an event will occur equals the number of favorable ways divided by the total number of ways. If P is the probability, m is the number of favorable ways, and n is the total number of ways, then P m n For example: What is the probability that a head will turn up on a single throw of a penny? The favorable number of ways is 1 (a head). 1 The total number of ways is 2 (a head and a tail). Thus, the probability is . 2 If a and b are two mutually exclusive events, then the probability that a or b will occur is the sum of the individual probabilities. Suppose Pa is the probability that an event a occurs. Suppose that Pb is the probability that a second independent event b occurs. Then the probability that the first event a occurs and the second event b occurs subsequently is Pa Pb.

The Absolute Value Sign 615. The symbol denotes absolute value. The absolute value of a number is the numerical value of the number without the plus or minus sign in front of it. Thus all absolute values are positive. For example, 3 is 3, and 2 is 2. Here’s another example: If x is positive and y is negative x y x y.

Functions 616. Suppose we have a function of x. This is denoted as f(x) (or g( y) or h(z) etc.). As an example, if f(x) x then f(3) 3. In this example we substitute the value 3 wherever x appears in the function. Similarly f (2) 2. Consider another example: If f ( y) y 2 y, then f(2) 22 2 2. f(2) (2)2 (2) 6. f(z) z2 z. f(2z) (2z)2 (2z) 4z2 2z. Let us consider still another example: Let f(x) x 2 and g(y) 2y. What is f [ g(2)]? Now 1 1 1 1 1 g(2) 22 . Thus f [g(2)] f . Since f (x) x 2, f 2 2 . 4 4 4 4 4

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Practice Test 6 Miscellaneous Problems Including Averages, Series, Properties of Integers, Approximations, Probability, the Absolute Value Sign, and Functions Correct answers and solutions follow each test. 1.

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1. If n is the first of five consecutive odd numbers, what is their average?

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n n1 n2 n3 n4

2. What is the average of the following numbers: 35.5, 32.5, 34.0, 35.0, 34.5?

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33.0 33.8 34.0 34.3 34.5

3. What is the next number in the following series: 1, 5, 9, 13, . . . ?

(A) (B) (C) (D) (E)

11 15 17 19 21

4. Which of the following is the next number in the series: 3, 6, 4, 9, 5, 12, 6, . . . ?

(A) (B) (C) (D) (E) 5.

If P is an even number, and Q and R are both odd, which of the following must be true? (A) (B) (C) (D) (E)

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P • Q is an odd number Q R is an even number PQ PR is an odd number Q R cannot equal P P Q cannot equal R

If a number is divisible by 102, then it is also divisible by: (A) (B) (C) (D) (E)

23 11 103 5 2

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Which of the following numbers is divisible by 36? (A) (B) (C) (D) (E)

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How many prime numbers are there between 45 and 72? (A) (B) (C) (D) (E)

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0.3700 3.700 37.00 370.0 3700

In a class with six boys and four girls, the students all took the same test. The boys’ scores were 74, 82, 84, 84, 88, and 95 while the girls’ scores were 80, 82, 86, and 86. Which of the following statements is true? (A) (B) (C) (D) (E)

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7.40096 10.0342 Which of the following best approximates ? .2001355 (A) (B) (C) (D) (E)

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2 Which of the following represents the smallest possible value of (M 1) , if M is an 2 integer?

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35,924 64,530 74,098 152,640 192,042

The boys’ average was 0.1 higher than the average for the whole class. The girls’ average was 0.1 lower than the boys’ average. The class average was 1.0 higher than the boys’ average. The boys’ average was 1.0 higher than the class average. The girls’ average was 1.0 lower than the boys’ average.

If the following series continues to follow the same pattern, what will be the next number: 2, 6, 3, 9, 6, . . . ? (A) (B) (C) (D) (E)

3 6 12 14 18

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13. Which of the following numbers must be odd?

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14. Which of the following numbers is the best approximation of the length of one side of

a square with an area of 12 square inches? (A) (B) (C) (D) (E)

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3.2 inches 3.3 inches 3.4 inches 3.5 inches 3.6 inches

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sented by n2 2n 1? (A) (B) (C) (D) (E)

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The sum of an odd number and an odd number. The product of an odd number and an even number. The sum of an odd number and an even number. The product of two even numbers. The sum of two even numbers.

It can be odd or even. It must be odd. It must be divisible by four. It must be divisible by six. The answer cannot be determined from the given information.

16. What is the next number in the series: 2, 5, 7, 8, . . . ?

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8 9 10 11 12 1 2

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17. What is the average of the following numbers: 3 , 4 , 2 , 3 , 4?

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3.25 3.35 3.45 3.50 3.60

18. Which of the following numbers is divisible by 24?

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76,300 78,132 80,424 81,234 83,636

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19. In order to graduate, a boy needs an average of 65 percent for his five major subjects.

His first four grades were 55, 60, 65, and 65. What grade does he need in the fifth subject in order to graduate? (A) (B) (C) (D) (E)

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2t 2t 3 3t 2t 2 t1

21. If the average of five whole numbers is an even number, which of the following state-

ments is not true? (A) (B) (C) (D) (E)

22.

65 70 75 80 85

The sum of the five numbers must be divisible by 2. The sum of the five numbers must be divisible by 5. The sum of the five numbers must be divisible by 10. At least one of the five numbers must be even. All of the five numbers must be odd.

22. What is the product of 23 and 79 to one place of accuracy?

(A) (B) (C) (D) (E)

1,600 1,817 1,000 1,800 2,000

23. What is the next term in the series 1, 1, 2, 3, 5, 8, 13, . . . ?

(A) (B) (C) (D) (E)

18 21 13 9 20

24. What is the next number in the series 1, 4, 2, 8, 6, . . . ?

(A) (B) (C) (D) (E)

4 6 8 15 24 1

25. Which of the following is closest to the square root of ?

2

(A) (B) (C) (D) (E)

0.25 0.5 0.6 0.7 0.8

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26.

27.

A

B

C

D

E

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A

B

C

D

E

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26. How many prime numbers are there between 56 and 100?

(A) (B) (C) (D) (E)

27. If you multiply one million, two hundred thousand, one hundred seventy-six by five

hundred twenty thousand, two hundred four, and then divide the product by one billion, your result will be closest to: (A) (B) (C) (D) (E)

28.

29.

A

B

C

D

E

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A

B

C

D

E

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31.

32.

A

B

C

D

E

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A

B

C

D

E

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A

B

C

D

E

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0.6 6 600 6,000 6,000,000

28. The number 89.999 rounded off to the nearest tenth is equal to which of the following?

(A) (B) (C) (D) (E)

90.0 89.0 89.9 89.99 89.90

29. a, b, c, d, and e are integers; M is their average; and S is their sum. What is the ratio

of S to M? (A) (B) (C) (D) (E)

30.

8 9 10 11 None of the above.

1:5 5:1 1:1 2:1 depends on the values of a, b, c, d, and e

30. What is the next number in the series 1, 1, 2, 4, 5, 25, . . . ?

(A) (B) (C) (D) (E)

8 12 15 24 26

31. The sum of five odd numbers is always:

(A) (B) (C) (D) (E)

even divisible by three divisible by five a prime number None of the above.

32. If E is an even number, and F is divisible by three, then what is the largest number by

which E 2F 3 must be divisible? (A) (B) (C) (D) (E)

6 12 54 108 144

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33.

A

B

C

D

E

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33. If the average of five consecutive even numbers is 8, which of the following is the

smallest of the five numbers? (A) (B) (C) (D) (E)

34.

35.

36.

37.

A

B

C

D

E

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A

B

C

D

E

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A

B

C

D

E

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A

B

C

D

E

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34. What is the next number in the sequence 1, 4, 7, 10, . . . ?

(A) (B) (C) (D) (E)

39.

A

B

C

D

E

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A

B

C

D

E

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13 14 15 16 18

35. If a number is divisible by 23, then it is also divisible by which of the following?

(A) (B) (C) (D) (E)


36. What is the next term in the series 3, 6, 2, 7, 1, . . . ?

(A) (B) (C) (D) (E)

0 1 3 6 8

37. What is the average (to the nearest tenth) of the following numbers: 91.4, 91.5, 91.6,

91.7, 91.7, 92.0, 92.1, 92.3, 92.3, 92.4? (A) (B) (C) (D) (E)

38.


91.9 92.0 92.1 92.2 92.3

38. What is the next term in the following series: 8, 3, 10, 9, 12, 27, . . . ?

(A) (B) (C) (D) (E)

8 14 18 36 81


(A) (B) (C) (D) (E)

30,217 44,221 59,403 60,411 None of the above.

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40.

41.

A

B

C

D

E

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A

B

C

D

E

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40. What is the next number in the series 1, 4, 9, 16, . . . ?

(A) (B) (C) (D) (E)

41. Which of the following is the best approximation of the product (1.005) (20.0025)

(0.0102)? (A) (B) (C) (D) (E)

42.

43.

44.

45.

46.

A

B

C

D

E

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A

B

C

D

E

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A

B

C

D

E

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A

B

C

D

E

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A

B

C

D

E

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22 23 24 34 25

0.02 0.2 2.0 20 200

42. What is the next number in the series 5, 2, 4, 2, 3, 2, . . . ?

(A) (B) (C) (D) (E)

1 2 3 4 5

43. If a, b, and c are all divisible by 8, then their average must be

(A) (B) (C) (D) (E)

divisible by 8 divisible by 4 divisible by 2 an integer None of the above.


(A) (B) (C) (D) (E)

13,944 15,746 15,966 16,012 None of the above.

45. Which of the following numbers is a prime?

(A) (B) (C) (D) (E)

147 149 153 155 161

46. What is the next number in the following series: 4, 8, 2, 4, 1, . . . ?

(A) (B) (C) (D) (E)

1 2 4 8 16

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47.

48.

A

B

C

D

E

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A

B

C

D

E

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47. The sum of four consecutive odd integers must be:

(A) (B) (C) (D) (E)

even, but not necessarily divisible by 4 divisible by 4, but not necessarily by 8 divisible by 8, but not necessarily by 16 divisible by 16 None of the above.

1 (A) 2 2 (B) 3 3 (C) 4 4 (D) 5 (E) 1

49.

50.

A

B

C

D

E

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A

B

C

D

E

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3 5

48. Which of the following is closest to the square root of ?

49. What is the next term in the series: 9, 8, 6, 3, . . . ?

(A) (B) (C) (D) (E)

0 2 1 3 1

50. The sum of an odd and an even number is

(A) (B) (C) (D) (E)

a perfect square negative even odd None of the above.

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E D C D B E D C B D E E C

14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.

D C A C C D B E E B E D B

27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38.

C A B E E D A A E E A B

39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.

A E B B E A B B C C E D


Choice E is correct. The five consecutive odd numbers must be n, n 2, n 6, and n 8. Their average is equal to their sum, 5n 20, divided by the number of addends, 5, which yields n 4 as the average. (601)

2.

Choice D is correct. Choosing 34 as an approximate average results in the following addends: 1.5, 1.5, 0, 1.0, and 0.5. Their sum is 1.5. Now, divide by 5 to get 0.3 and add this to 34 to get 34.3. (To check this, add the five original numbers and divide by 5.) (601)

3.

Choice C is correct. This is an arithmetic sequence: Each term is 4 more than the preceding one. The next term is 13 4 or 17. (602)

4.

Choice D is correct. This series can be divided into two parts: the even-numbered terms: 6, 9, 12, . . . and the odd-numbered terms: 3, 4, 5, 6, . . . (Even- and odd-numbered terms refers to the terms’ place in the series and not if the term itself is even or odd.) The next term in the series is even-numbered, so it will be formed by adding 3 to the 12 (the last of the even-numbered terms) to get 15. (602)

5.

Choice B is correct. Since Q is an odd number, it may be represented by 2m 1, where m is an integer. Similarly, call R, 2n 1 where n is an integer. Thus, Q R is equal to (2m 1) (2n 1), 2m 2n, or 2(m n). Now, since m and n are integers, m n will be some integer p. Thus, Q R 5 2p. Any number in the form of 2p, where p is any integer, is an even number. Therefore, Q R must be even. (A) and (C) are wrong, because an even number multiplied by an odd is always even. (D) and (E) are only true for specific values of P, Q, and R. (604)

6.

Choice E is correct. If a number is divisible by 102 then it must be divisible by all of the factors of 102. The only choice that is a factor of 102 is 2. (607)

7.

Choice D is correct. To be divisible by 36, a number must be divisible by both 4 and 9. Only (A) and (D) are divisible by 4. (Recall that only the last two digits must be examined.) Of these, only (D) is divisible by 9. (The sum of the digits of (A) is 23, which is not divisible by 9; the sum of the digits of (D) is 18.) (607)

8.

Choice C is correct. The prime numbers between 45 and 72 are 47, 53, 59, 61, 67, and 71. All of the others have factors other than 1 and themselves. (608)

9.

Choice B is correct. Since M must be an integer, the closest value it can have to 1 is either 1 2 1 1 2 (409) or 0. In either case, ( M ) is equal to , or 0.25. 4 2

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10.

11.

Choice D is correct. Approximate to only one place (this is permissible, because the choices are so far apart; if they had been closer together, two or three places would have been used). 7 10 , which is equal to 350. This is closest to After this approximation, the expression is: 0.2 370. (609) 74 82 84 84 88 95 Choice E is correct. The average for the boys alone was , 6 80 82 86 86 or 507 6 84.5. The girls’ average was , or 334 4 83.5, which is 4 1.0 below the boys’ average. (601)

12.

Choice E is correct. To generate this series, start with 2; multiply by 3 to get 6; subtract 3 to get 3; multiply by 3; subtract 3; etc. Thus, the next term will be found by multiplying the previous term, 6, by 3 to get 18. (602)

13.

Choice C is correct. The sum of an odd number and an even number can be expressed as (2n 1) (2m), where n and m are integers. (2n 1 must be odd, and 2m must be even.) Their sum is equal to 2n 2m 1, or 2 (m n) 1. Since (m n) is an integer, the quantity 2(m n) 1 must represent an odd integer. (604, 605)

14.

Choice D is correct. The actual length of one of the sides would be the square root of 12. Square each of the five choices to find the square of 3.4 is 11.56, and the square of 3.5 is 12.25. The square root of 12 must lie between 3.4 and 3.5. Squaring 3.45 (halfway between the two choices) yields 11.9025, which is less than 12. Thus the square root of 12 must be greater than 3.45 and therefore closer to 3.5 than to 3.4. (612)

15.

Choice C is correct. Factor n2 2n 1 to (n 1)(n 1) or (n 1)2. Now, since n is an odd number, n 1 must be even (the number after every odd number is even). Thus, representing n 1 as 2k where k is an integer (2k is the standard representation for an even number) yields the expression: (n 1)2 (2k)2 or 4k2. Thus, (n 1)2 is a multiple of 4, and it must be divisible by 4. A number divisible by 4 must also be even, so (C) is the best choice. (604–607)

16.

Choice A is correct. The differences between terms are as follows: 3, 2, and 1. Thus, the next term should be found by adding 0, leaving a result of 8. (602)

17.

Choice C is correct. Convert to decimals. Then calculate the value of: 3.50 4.25 2.25 3.25 4.00 . This equals 17.25 5, or 3.45. 5

(601)

18.

Choice C is correct. If a number is divisible by 24, it must be divisible by 3 and 8. Of the five choices given, only choice (C) is divisible by 8. Add the digits in 80,424 to get 18. As this is divisible by 3, the number is divisible by 3. The number, therefore, is divisible by 24. (607)

19.

Choice D is correct. If the boy is to average 65 for five subjects, the total of his five grades must be five times 65 or 325. The sum of the first four grades is 55 60 65 65, or 245. Therefore, the fifth mark must be 325 245, or 80. (601)

20.

Choice B is correct. If t is any integer, then 2t is an even number. Adding 3 to an even number always produces an odd number. Thus, 2t 3 is always odd. (606)

21.

Choice E is correct. Call the five numbers, a, b, c, d, and e. Then the average is (a b c d e) (a b c d e) . Since this must be even, 2k, where k is an 5 5 integer. Thus a b c d e 10k. Therefore, the sum of the 5 numbers is divisible by 10, 2, and 5. Thus the first three choices are eliminated. If the five numbers were 1, 1, 1, 1,

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and 6, then the average would be 2. Thus, the average is even, but not all of the numbers are even. Thus, choice (D) can be true. If all the numbers were odd, the sum would have to be odd. This contradicts the statement that the average is even. Thus, choice (E) is the answer. (601, 607) 22.

Choice E is correct. First, round off 23 and 79 to one place of accuracy. The numbers become 20 and 80. The product of these two numbers is 1,600, which rounded off to one place is 2,000. (611)

23.

Choice B is correct. Each term in this series is the sum of the two previous terms. Thus, the next term is 8 13 or 21. (602)

24.

Choice E is correct. This series can be generated by the following steps: multiply by 4; subtract 2; multiply by 4; subtract 2; etc. Since the term “6” was obtained by subtracting 2, multiply by 4 to obtain 4 6 24, the next term. (602)

25.

Choice D is correct. 0.7 squared is 0.49. Squaring 0.8 yields 0.64. Thus, the square root of 1 must lie between 0.7 and 0.8. Take the number halfway between these two, 0.75, and 2 1 square it. This number, 0.5625, is more than , so the square root must be closer to 0.7 than 2 to 0.8. An easier way to do problems concerning the square roots of 2 and 3 and their multiples is to memorize the values of these two square roots. The square root of 2 is about 1.414 (remember fourteen-fourteen), and the square root of three is about 1.732 (remember 1 1 that 1732 was the year of George Washington’s birth). Apply these as follows: 2. 2 4 1 1 1 1.414 0.707, which is very close to 0.7. (612) Thus, 2 2 2 4

26.

Choice B is correct. The prime numbers can be found by taking all the odd numbers between 56 and 100 (the even ones cannot be primes) and eliminating all the ones divisible by 3, by 5, and by 7. If a number under 100 is divisible by none of these, it must be prime. Thus, the only primes between 56 and 100 are 59, 61, 67, 71, 73, 79, 83, 89, and 97. (608)

27.

Choice C is correct. Since all the answer requires is an order-of-ten approximation, do not calculate the exact answer. Approximate the answer in the following manner: 1,000,000 500,000 500. The only choice on the same order of magnitude is 600. (609) 1,000,000,000

28.

Choice A is correct. To round off 89.999, look at the number in the hundredths’ place. 9 is more than 5, so add 1 to the number in the tenths’ place and eliminate all of the digits to the right. Thus, we get 90.0. (609)

29.

Choice B is correct. The average of five numbers is found by dividing their sum by five. Thus, the sum is five times the average, so S : M 5 : 1. (601)

30.

Choice E is correct. The series can be generated by the following steps: To get the second term, square the first term; to get the third, add 1 to the second; to get the fourth, square the third; to get the fifth, add 1 to the fourth; etc. The pattern can be written as: square; add 1; repeat the cycle. Following this pattern, the seventh term is found by adding one to the sixth term. Thus, the seventh term is 1 25, or 26. (602)

31.

Choice E is correct. None of the first four choices is necessarily true. The sum, 5 7 9 13 15 49, is not even, divisible by 3, divisible by 5, nor prime. (604, 607, 608)

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32.

Choice D is correct. Any even number can be written as 2m, and any number divisible by 3 can be written as 3n, where m and n are integers. Thus, E 2F 3 equals (2m)2 (3n)3 (4m2) (27n3) 108(m2n3), and 108 is the largest number by which E 2F 3 must be divisible. (607)

33.

Choice A is correct. The five consecutive even numbers can be represented as n, n 2, n 4, n 6, and n 8. Taking the sum and dividing by five yields an average of n 4. Thus, n 4 8, the given average, and n 4, the smallest number. (601)

34.

Choice A is correct. To find the next number in this sequence, add 3 to the previous number. This is an arithmetic progression. The next term is 10 3, or 13. (602)

35.

Choice E is correct. If a number is divisible by 23, then it is divisible by all of the factors of 23. But 23 is a prime with no factors except 1 and itself. Therefore, the correct choice is (E). (607)

36.

Choice E is correct. The steps generating the successive terms in this series are (to the previous term): add 3; subtract 4; add 5; subtract 6; add 7; etc. The next term is 1 7 8. (602)

37.

Choice A is correct. To find the average, it is convenient to choose 92.0 as an approximate average and then find the average of the differences between the actual numbers and 92.0. Thus, add up: (0.6) ( 0.5) ( 0.4) ( 0.3) ( 0.3) (0.0) 0.1 0.3 0.3 0.4, to 1.0; divide this by ten (the number of quantities to be averaged) to obtain 0.1. Finally, add this to the approximate average, 92.0, to obtain a final average of 91.9. (601)

38.

Choice B is correct. This series is a combination of two sub-series: The odd-numbered terms, 3, 9, 27, etc., form a geometric series; the even-numbered terms, 8, 10, 12, 14, etc., form an arithmetic sequence. The next number in the sequence is from the arithmetic sequence and is 14. (Note that in the absence of any other indication, assume a series to be as simple as possible, i.e., arithmetic or geometric.) (602)

39.

Choice A is correct. To determine if a number is divisible by 11, take each of the digits separately and, beginning with either end, subtract the second from the first, add the following digit, subtract the next one, add the one after that, etc. If this result is divisible by 11, the entire number is. Thus, because 3 0 2 1 7 11, we know that 30,217 is divisible by 11. Using the same method, we find that the other four choices are not divisible by 11. (607)

40.

Choice E is correct. This is the series of integers squared. 12, 22, 32, 42 . . . the next term is 52 or 25. (602)

41.

Choice B is correct. This is simply an order-of-ten approximation, so round off the numbers and work the following problem. (1.0)(20.0)(0.01) 0.20. The actual answer is closest to 0.2. (611)

42.

Choice B is correct. The even-numbered terms of this series form the sub-series: 2, 2, 2, . . . The odd-numbered terms form the arithmetic series: 5, 4, 3, 2 , . . . The next term in the series is a 2. (602)

43.

Choice E is correct. Represent the three numbers as 8p, 8q, and 8r, respectively. Thus, their (8p 8q 8r) sum is 8p 8q 8r, and their average is . This need not even be a whole 3 2 56 (601, 607) number. For example, the average of 8, 16, and 32 is , or 18 . 3 3

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44.

Choice A is correct. To be divisible by 24, a number must be divisible by both 3 and 8. Only 13,944 and 15,966 are divisible by 3; of these, only 13,944 is divisible by 8 (13,944 24 581). (607)

45.

Choice B is correct. The approximate square root of each of these numbers is 13. Merely divide each of these numbers by the primes up to 13, which are 2, 3, 5, 7, and 11. The only number not divisible by any of these primes is 149. (608, 612)

46.

Choice B is correct. The sequence is formed by the following operations: Multiply by 2, divide by 4, multiply by 2, divide by 4, etc. Accordingly, the next number is 1 2, or 2. (602)

47.

Choice C is correct. Call the first odd integer 2k 1. (This is the standard representation for a general odd integer.) Thus, the next 3 odd integers are 2k 3, 2k 5, and 2k 7. (Each one is 2 more than the previous one.) The sum of these integers is (2k 1) (2k 3) (2k 5) (2k 7) 8k 16. This can be written as 8(k 2), which is divisible by 8, but not necessarily by 16. (606, 607)

48.

Choice C is correct. By squaring the five choices, it is evident that the two closest choices 3 2 4 2 3 4 are: 0.5625 and 0.64. Squaring the number halfway between and gives 4 5 4 5 3 3 3 (0.775)2 0.600625. This is greater than , so the square root of must be closer to than 5 5 4 4 (612) to . 5

49.

Choice E is correct. The terms decrease by 1, then 2, then 3, so the next term is 4 less than 3, or 1. (602)

50.

Choice D is correct. Let the even number be 2k, where k is an integer, and let the odd number be 2m 1, where m is an integer. Thus, the sum is 2k (2m 1), 2k 2m 1, or 2(k m) 1. Now k m is an integer since k and m are integers. Call k m by another name, p. Thus, 2(k m) 1 is 2p 1, which is the representation of an odd number. (604, 606)

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Tables, Charts, and Graphs

Charts and Graphs 701. Graphs and charts show the relationship of numbers and quantities in visual form. By looking at a graph, you can see at a glance the relationship between two or more sets of information. If such information were presented in written form, it would be hard to read and understand. Here are some things to remember when doing problems based on graphs or charts: 1.

Understand what you are being asked to do before you begin figuring.

2.

Check the dates and types of information required. Be sure that you are looking in the proper columns, and on the proper lines, for the information you need.

3.

Check the units required. Be sure that your answer is in thousands, millions, or whatever the question calls for.

4.

In computing averages, be sure that you add the figures you need and no others, and that you divide by the correct number of years or other units.

5.

Be careful in computing problems asking for percentages. (a) Remember that to convert a decimal into a percent you must multiply it by 100. For example, 0.04 is 4%. (b) Be sure that you can distinguish between such quantities as 1% (1 percent) and .01% (one one-hundredth of 1 percent), whether in numerals or in words. (c) Remember that if quantity X is greater than quantity Y, and the question asks what percent quantity X is of quantity Y, the answer must be greater than 100 percent.

Tables and Charts 702. A table or chart shows data in the form of a box of numbers or chart of numbers. Each line describes how the numbers are connected. Example: Test Score

Number of Students

90 85 80 60

2 1 1 3

Example: How many students took the test? Solution: To find out the number of students that took the test, just add up the numbers in the column marked “Number of Students.” That is, add 2 1 1 3 7.

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Example: What was the difference in score between the highest and the lowest score? Solution: First look at the highest score: 90. Then look at the lowest score: 60. Now calculate the difference: 90 60 30. ian score? Example: What was the med Solution: The median score means the score that is in the middle of all the scores. That is, there are just as many scores above the median as below it. So in this example, the scores are 90, 90 (there are two 90’s) 85, 80, and 60, 60, 60 (there are three 60’s). So we have: 90 90 85 80 60 60 60 80 is right in the middle. That is, there are three scores above it and three scores below it. So 80 is the median. Example: What was the mean score? Solution: The mean score is defined as the average score. That is, it is the sum of the scores total number of scores The sum of the scores is 90 90 85 80 60 60 60 525. The total number of scores is 2 1 1 3 7, so divide 7 into 525 to get the average: 75.

Graphs 703. To read a graph, you must know what scale the graph has been drawn to. Somewhere on the face of the graph will be an explanation of what each division of the graph means. Sometimes the divisions will be labeled. At other times, this information will be given in a small box called a scale or legend. For instance, a map, which is a specialized kind of graph, will always carry a scale 1 or legend on its face telling you such information as 1 100 miles or 2 miles. 4

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Bar Graphs 704. The bar graph shows how the information is compared by using broad lines, called bars, of varying lengths. Sometimes single lines are used as well. Bar graphs are good for showing a quick comparison of the information involved, however, the bars are difficult to read accurately unless the end of the bar falls exactly on one of the divisions of the scale. If the end of the bar falls between divisions of the scale, it is not easy to arrive at the precise figure represented by the bar. In bar graphs, the bars can run either vertically or horizontally. The sample bar graph following is a horizontal graph. EXPENDITURES PER PUPIL —1990

The individual bars in this kind of graph may carry a label within the bar, as in this example. The label may also appear alongside each bar. The scale used on the bars may appear along one axis, as in the example, or it may be noted somewhere on the face of the graph. Each numbered space on the x- (or horizontal) axis represents an expenditure of $10 per pupil. A wide variety of questions may be answered by a bar graph, such as: (1) Which area of the country spends least per pupil? Rocky Mountains. (2) How much does the New England area spend per pupil? $480. (3) How much less does the Great Plains spend per pupil than the Great Lakes? $464 447 $17/pupil. (4) How much more does New England spend on a pupil than the Rocky Mountain area? $480 433 $47/pupil.

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Circle Graphs 705. A circle graph shows how an entire quantity has been divided or apportioned. The circle represents 100 percent of the quantity; the different parts into which the whole has been divided are shown by sections, or wedges, of the circle. Circle graphs are good for showing how money is distributed or collected, and for this reason they are widely used in financial graphing. The information is usually presented on the face of each section, telling you exactly what the section stands for and the value of that section in comparison to the other parts of the graph. SOURCES OF INCOME—PUBLIC COLLEGES OF U.S.

*Government refers to all levels of government—not exclusively the federal government. The circle graph above indicates where the money originates that is used to maintain public colleges in the United States. The size of the sections tells you at a glance which source is most important (government) and which is least important (endowments). The sections total 100¢ or $1.00. This graph may be used to answer the following questions: (1) What is the most important source of income to the public colleges? Government. (2) What part of the revenue dollar comes from tuition? 10¢. 2 (3) Dormitory fees bring in how many times the money that endowments bring in? 5 times 3 17 2 5 . 3 3 (4) What is the least important source of revenue to public colleges? Endowments.

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Line Graphs 706. Graphs that have information running both across (horizontally) and up and down (vertically) can be considered to be laid out on a grid having a y-axis and an x-axis. One of the two quantities being compared will be placed along the y-axis, and the other quantity will be placed along the x-axis. When we are asked to compare two values, we subtract the smaller from the larger. SHARES OF STOCK SOLD NEW YORK STOCK EXCHANGE DURING ONE SIX-MONTH PERIOD

Our sample line graph represents the total shares of stock sold on the New York Stock Exchange between January and June. The months are placed along the x-axis, while the sales, in units of 1,000,000 shares, are placed along the y-axis. (1) How many shares were sold in March? 225,000,000. (2) What is the trend of stock sales between April and May? The volume of sales rose. (3) Compare the share sales in January and February. 25,000,000 fewer shares were sold in February. (4) During which months of the period was the increase in sales largest? February to March.

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Practice Test 7

5.

Tables, Charts, and Graphs Practice Tests

(A) (B) (C) (D) (E)

TABLE CHART TEST Questions 1–5 are based on this table chart.

1.

3 4 2 3 2 3 4

8 16 23 32 38 44 50

32 29 25 21 50

75% 60% 58% 29% 80%

According to the chart, which week was the worst for the team? (A) (B) (C) (D) (E)

4.

5 4 5 6 4 3 2

Choice B is correct. To find the total number of games won, add the number of games won for all the weeks, 5 4 5 6 4 3 2 29. (702)

2.

Choice C is correct. The team won 29 out of 50 games or 58%. (702)

3.

Choice E is correct. The seventh week was the only week that the team lost more games than it won. (702)

4.

Choice B is correct. During the third week the team won 5 games and lost 2, or it won about 70% of the games that week. Compared with the winning percentages for other weeks, the third week’s was the highest. (702)

5.

Choice C is correct. To win 70% of all the games, the team must win 70 out of 100. Since it won 29 games out of the first 50 games, it must win 70 29 or 41 games out of the next 50 games. (702)

What percent of the games did the team win? (A) (B) (C) (D) (E)

3.

Games lost

1.

How many games did the team win during the first seven weeks? (A) (B) (C) (D) (E)

2.

Games won

Total No. of games played

39 35 41 34 32

Solutions

The following chart is a record of the performance of a baseball team for the first seven weeks of the season.

First Week Second Week Third Week Fourth Week Fifth Week Sixth Week Seventh Week

If there are fifty more games to play in the season, how many more games must the team win to end up winning 70% of the games?

second week fourth week fifth week sixth week seventh week

Which week was the best week for the team? (A) (B) (C) (D) (E)

first week third week fourth week fifth week sixth week

PIE CHART TEST Questions 1–5 are based on this pie chart.

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1.

Which region was the most populated region in 1964? (A) (B) (C) (D) (E)

2.

East North Central Middle Atlantic South Atlantic Pacific New England

What part of the entire population lived in the Mountain region? 1 (A) 10 1 (B) 30 1 (C) 50 1 (D) 25 1 (E) 8

3.

4.

Choice B is correct. Middle Atlantic had 18.8% and South Atlantic had 14.8% of the population. So, Middle Atlantic had 4.0% more. 4.0% of 191.3 million is .04 191.3 or about 7.7 million. (705)

5.

Choice C is correct. All the regions combined had 100% of the population or 191.3 million. (705)

LINE GRAPH TEST Questions 1–5 are based on this line graph.

20 million 24 million 30 million 28 million 15 million

Approximately how many more people lived in the Middle Atlantic region than in the South Atlantic? (A) (B) (C) (D) (E)

5.

Choice B is correct. Pacific had 12.5% of the population. 12.5% of 191.3 million is .125 191.3 or about 24 million. (705)

What was the approximate population in the Pacific region? (A) (B) (C) (D) (E)

4.

3.

4.0 million 7.7 million 5.2 million 9.3 million 8.5 million

On the ratio scale what were consumer prices recorded as of the end of 1985? (A) (B) (C) (D) (E)

What was the total population in all the regions combined? (A) (B) (C) (D) (E)

1.

2.

73.3 million 100.0 million 191.3 million 126.8 million 98.5 million

Solutions 1.

Choice A is correct. East North Central with 19.7% of the total population had the largest population. (705)

2.

Choice D is correct. The Mountain region had 4.0% 1 (705) of the population. 4.0% is . 25

During what year did consumer prices rise fastest? (A) (B) (C) (D) (E)

3.

95 100 105 110 115

1983 1985 1987 1988 1989

When wholesale and industrial prices were recorded as 110, consumer prices were recorded as (A) (B) (C) (D) (E)

between 125 and 120 between 120 and 115 between 115 and 110 between 110 and 105 between 105 and 100

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4.

For the 8 years 1982–1989 inclusive, the average increase in consumer prices was (A) (B) (C) (D) (E)

5.

BAR GRAPH TEST Questions 1–3 are based on this bar graph.

1 point 2 points 3 points 4 points 5 points

The percentage increase in wholesale and industrial prices between the beginning of 1982 and the end of 1989 was (A) (B) (C) (D) (E)

1 percent 5 percent 10 percent 15 percent less than 1 percent

Solutions 1.

Choice D is correct. Drawing a vertical line at the end of 1985, we reach the consumer price graph at about the 110 level. (706)

2.

Choice E is correct. The slope of the consumer graph is clearly steepest in 1989. (706)

3.

Choice A is correct. Wholesale and industrial prices were about 110 at the beginning of 1989, when consumer prices were between 120 and 125. (706)

4.

5.

1.

Choice C is correct. At the beginning of 1982 consumer prices were about 105; at the end of 1989 they 130 105 were about 130. The average increase is 8 25 or about 3. (706) 8 Choice D is correct. At the beginning of 1982 wholesale prices were about 100; at the end of 1989 they were about 115. The percent increase is about 115 100 100% or 15%. (706) 100

What was the ratio of soft plywood produced in 1978 as compared with that produced in 1987? (A) (B) (C) (D) (E)

2.

1:1 2:3 1:2 3:4 1:3

For the years 1978 through 1983, excluding 1982, how many billion square feet of plywood were produced altogether? (A) (B) (C) (D) (E)

23.2 29.7 34.1 40.7 50.5

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3.

Between which consecutive odd years and between which consecutive even years was the plywood production jump greatest? (A) (B) (C) (D) (E)

CUMULATIVE GRAPH TEST Questions 1–5 are based on this cumulative graph.

1985 and 1987; 1978 and 1980 1983 and 1985; 1984 and 1986 1979 and 1981; 1980 and 1982 1981 and 1983; 1980 and 1982 1983 and 1985; 1982 and 1984

Solutions 1.

Choice C is correct. To answer this question, you will have to measure the bars. In 1978, 8 billion square feet of plywood were produced. In 1987, 14 billion square feet were produced. The ratio of 8 : 14 is the same as 4 : 7. (704)

2.

Choice D is correct. All you have to do is to measure the bar for each year—of course, don’t include the 1982 bar—and estimate the length of each bar. Then you add the five lengths. 1978 8, 1979 10, 1980 10, 1981 10, 1983 12. The total is 50. (704)

3. Choice E is correct. The jump from 1983 to 1985

was from 12 to 14 2 billion square feet. The jump from 1982 to 1984 was from 11 to 13.5 2.5 billion square feet. None of the other choices show such broad jumps. (704)

1.

About how much in government funds was spent for research and development in 1987? (A) (B) (C) (D) (E)

$16 billion $8 billion $12 billion $24 billion $4 billion

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2.

Solutions

In 1987, about what percent of the total spending in research and development were company funds? 1.

Choice B is correct. Total spending was about $16 billion, and company spending was $8 billion. So, government spending was about $8 billion. (706)

2.

3. What was the change in the relative number of

Choice D is correct. Company funds totaled $8 billion, and the total funds were $16 billion. So, com1 (706) pany funds were of total funds or 50%. 2

research and development scientists and engineers with respect to all employees from 1984 to 1985?

3. Choice E is correct. The graph showing the rela-

(A) 40% (B) 25% 1 (C) 33 % 3 (D) 50% (E) 20%

(A) (B) (C) (D) (E)

10% 5% 2% 3% 0%

tive employment of research and development scientists and engineers was horizontal between 1984 and 1985. This means no change. (706) 4.

Choice B is correct. Company funds totaled $8 billion in 1987 and $2 billion in 1973. The increase was $6 billion. (706)

4. What was the increase in company funds in

research and development from 1973 to 1987? (A) (B) (C) (D) (E) 5.

$12 billion $6 billion $8 billion $4 billion $14 billion

What was the percent of increase of the company funds spent in research and development from 1973 to 1987? (A) (B) (C) (D) (E)

100% 50% 300% 400% 1,000%

5. Choice C is correct. Company funds totaled $2 bil-

lion in 1973, and the increase from 1973 to 1987 was $6 billion or 300% of $2 billion. (706)

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Modern Math Including Sets, Relations, Solution Sets, Closed Sets, and Axioms Sets 801. A set is a collection of anything: numbers, letters, objects, etc. The members, or elements of the set are written between braces like this: {1, 2, 3, 4, 5}. The elements of this set are simply the numbers 1, 2, 3, 4, and 5. Another example of a set is {apples, peaches, pears}. Two sets are equal if they have the same elements. The order in which the elements of the set are listed does not matter. Thus {1, 2, 3, 4, 5} {5, 4, 3, 2, 1}. We can use one letter to stand for a whole set; for example, A {1, 2, 3, 4, 5}. 802.

To find the union of two sets:

Write down every member in one or both of the two sets. The union of two sets is a new set. The union of sets A and B is written A B. For example: If A {1, 2, 3, 4} and B {2, 4, 6} find A B. All the elements in either A or B or both are 1, 2, 3, 4, and 6. Therefore A B {1, 2, 3, 4, 6}. 803.

To find the intersection of two sets:

Write down every member that the two sets have in common. The intersection of the sets A and B is a set written A B. For example: If A {1, 2, 3, 4} and B {2, 4, 6}, find A B. The elements in both A and B are 2 and 4. Therefore A B {2, 4}.

If two sets have no elements in common, then their intersection is the null or empty set, written as .

For example: The intersection of {1, 3, 5, 7} with {2, 4, 6, 8) is since they have no members in common. 804. To perform several union and intersection operations, first operate on sets within parentheses. For example: If A {1, 2, 3} and B {2, 3, 4, 5, 6} and C {1, 4, 6} find A (B C). First we find B C by listing all the elements in both B and C. B C {4, 6}. Then A (B C) is just the set of all members in at least one of the sets A and {4, 6}. Therefore, A (B C) {1, 2, 3, 4, 6}. 805. A subset of a set is a set, all of whose members are in the original set. Thus, {1, 2, 3} is a subset of the set {1, 2, 3, 4, 5}. Note that the null set is a subset of every set, and also that every set is a subset of itself. In general, a set with n elements has 2n subsets. For example: How many subsets does {x, y, z} have? This set has 3 elements and therefore 23 or 8 subsets.

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Relations 806. When the elements of a set are ordered pairs, then the set is called a relation. An ordered pair is written (x, y). The order of the two components of the ordered pair matters. Therefore the ordered pairs (x, y) and (y, x) are not equal.

The domain of a relation is the set of the first components of the ordered pairs. The range of a relation is the set of the second components of the ordered pairs. A relation is a function if each element of the domain occurs only once as a first component.

For example: R {(a, b), (a, c), (b, c), (c, d)}. Find the domain and range of R. Is the relation R a function? The domain is the set of first components. These are a, a, b, and c, so that the domain is {a, b, c}. The range is the set of second components. These are b, c, c, and d. Thus the range is {b, c, d}. R is not a function since the letter a occurred twice as a first component. 807. The inverse of a relation is the relation with all the ordered pairs reversed. Thus, the inverse of R {(1, 2), (3, 4), (5, 6)} is {(2, 1), (4, 3), (6, 5)}. For example: Find the domain of the inverse of {(m, n), (p, q), (r, s)}. The domain of the inverse is simply the range of the original relation. So, the domain of the inverse is {n, q, s}. Similarly, the range of the inverse is the domain of the original relation.

Solution Sets 808. Sets can be used to indicate solutions to equations or inequalities. These sets are called solution sets. A solution set is just the set of the solutions to an equation. We may also demand that the elements of the solution set meet another condition. Thus, the solution set for the equation 10x 5 0 is simply {1⁄ 2}, since only x 1⁄ 2 solves the equation. If we demanded that the solution set consists only of whole numbers, then the solution set would be since no whole number solves this equation. The solution set in the positive integers (whole numbers) for the inequality x 4 is {1, 2, 3} since these are the only positive integers less than 4.

When finding a solution set, first solve the equation or inequality and then use only the solutions which satisfy the condition required.

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For example: Find the solution set in the positive integers for the inequality 4x x 13. First, 4x x 13 means 3x 13 or x 41⁄ 3. Since x must be a positive integer, the solution set is the set of positive integers less than 41⁄ 3, or {1, 2, 3, 4}. Sometimes we use the following notation: R {x : x 10} This would be read as “the set of all x such that x is greater than or equal to 10.”

Axioms 809. On your test, there may be a list of axioms, or rules, about arithmetical operations with numbers. The list will contain examples of the use of the axioms. Problems will then ask you to identify which axiom is used to make a specific statement. An example of these axioms is the distributive law. A problem may ask you: Which axiom is used to justify 3(4 1 ) 3 ⋅ 4 3 ⋅ 1? The distributive axiom is used to justify this statement. Another axiom is the commutative axiom of addition and multiplication. The equations 5 3 3 5 and 5 ⋅ 3 3 ⋅ 5 illustrate these rules. The last two rules are the associative axioms of addition and multiplication. Examples of these operations are the equations (3 5) 6 3 (5 6) and (3 ⋅ 5) 6 3(5 ⋅ 6).

Closed Sets 810. A set is called “closed” under an operation if, under the operation, any two members of the set constitute an element of the set. Consider, for example, the set {0, 1}. This set is closed under the operation of multiplication because 0 0 0, 1 1 1, and 0 1 0. Note that in order for the set to be closed, the elements multiplied by themselves must also be an element of the set {0 0 0 and 1 1 1}.

Mathematical Symbols ⋅ multiplication dot; as in x ⋅ y ( ) parentheses; used to group expressions % percent division symbol : ratio symbol equals does not equal less than greater than less than or equal to

greater than or equal to a square root symbol

pi, the ratio between the circumference and diameter of a circle; approximately equal to 22⁄ 7. angle is parallel to is perpendicular to and or not → implies belongs to is a subset of

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Practice Test 8 and Solutions Modern Math Correct answers and solutions follow each test.

Sets Test 1.

A {1, 2, 3, 4, 5} B {2, 4, 6, 8}. A B equals (A) {1, 2, 3, 4, 5, 6, 7, 8} (B) {2, 4} (C) {1, 2, 3, 4, 5, 6, 8, 10} (D) {9} (E) {1, 2, 6, 8}

3.

Use the following information to answer Questions 7–10. A {1, 3, 2, 5}. B {2, 4, 6}. 7.

(A B) C equals (A) {1, 2, 3} (B) {2, 4, 5} (C) {1, 2, 5} (D) {1, 3, 5} (E) {3, 4, 5}

A {1, 2, 3}. B {2, 3, 4}. C {3, 4, 5}. (A B) C equals

8.

How many elements are there in the set of even integers from 2 and 10 inclusive? (A) 3 (B) 5 (C) 7 (D) 9 (E) 10

(A B) C equals (A) {1, 2, 3, 5} (B) {4} (C) {2, 4} (D) {1, 3, 5} (E) {1, 2, 3, 4, 5}

9.

(A) {1, 2, 3, 4, 5} (B) {1, 3, 5} (C) {2, 3, 4} (D) {1} (E) {3} 5.

C {1, 3, 5}.

C {a, b, c, d}. D {3, 4, b}. C D equals (A) {a, b, c, d, 3, 4} (B) {b} (C) {3, 4} (D) {b, d, 4} (E) {a, c, 3, 4}

4.

How many subsets does {a, b, c} have? (A) 6 (B) 7 (C) 8 (D) 9 (E) 10

Which sets equals {1, 2, 3, 4}? (A) {a, b, c, d} (B) {4, 5, 6, 7} (C) {1, 3, 5, 7, 9} (D) {4, 3, 2, 1} (E) None of the above.

2.

6.

How many subsets does A (B C ) have? (A) 2 (B) 4 (C) 16 (D) 32 (E) 64

10.

Which set is not a subset of A C ? (A) (B) A (C) C (D) {4} (E) {1, 2, 5}

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Answers and Solutions 1.

(D) {4, 3, 2, 1} contains the same elements as {1, 2, 3, 4}. Since the order does not matter, the sets are equal. (801)

2.

(B) A B means the set of elements in both A and B or {2, 4}. (803)

3.

(A) C D means the set of elements in at least one of C and D, or {a, b, c, d, 3, 4}. (802)

4.

(E) (A B) C is the set of elements in all three sets. Only 3 is a member of all three sets, so (A B) C {3}. (803)

5.

(B) The set of even integers from 2 and 10 inclusive is {2, 4, 6, 8, 10} which has 5 elements. (801)

6.

(C) {a, b, c} has 3 elements and therefore 23 or 8 subsets. (805)

7.

(D) First (A B) {1, 2, 3, 4, 5, 6} Then {1, 2, 3, 4, 5, 6} {1, 3, 5} {1, 3, 5}.

(804)

(A) First (A B) {2} Then {2} {1, 3, 5} {1, 2, 3, 5}.

(804)

8.

9.

(E) A (B C) is the set of elements in at least one of the three sets, or {1, 2, 3, 4, 5, 6}, which has 26 or 64 subsets. (805)

10. (D) A C = {1, 2, 3, 5}. Since 4 is not an element of

this set, {4} is not a subset of A C.

(802, 805)

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Relations Test 1.

Which of the following sets are relations?

6.

I. {(1, 2), (a, c)} II. {(3, 8), 8, 3} III. {(1, a), (2, c)} (A) I only (B) II only (C) III only (D) I and III only (E) II and III only 2.

3.

What is the domain of {(1, 2), (2, 1), (1, 5)}? (A) {1, 2} (B) {(1, 2)} (C) {1, 2, 5} (D) {8} (E) {3}

5.

7.

Which relation is a function? (A) {(1, 1), (2, 2), (3, 3)} (B) {(1, 1), (1, 2), (1, 3)} (C) {(a, b), (b, a), (b, b)} (D) {(1, 3), (1, 5), (1, 7)} (E) {(1, a), (2, b), (2, 1)}

Which relation equals its inverse? (A) {(1, 2)} (B) {(1, 2), (3, 3)} (C) {(1, 2), (3, 3), (2, 1)} (D) {(4, 4), (2, 3), (3, 4)} (E) {(1, 2), (2, 3), (3, 1)}

8.

What is the domain of the inverse of {(a, 1), (b, 3), (c, 5)}? (A) {a, b, c} (B) {1, 3, 5} (C) {1, a, 2, b, 3, c} (D) {a, 5} (E) {(a, 5)}

What is the range of {(1, 2), (3, 4), (5, 6)}? (A) {1, 2, 3, 4, 5, 6} (B) {(1, 2)} (C) {(1, 2), (3, 4), (5, 6)} (D) {1, 3, 5} (E) None of the above.

4.

(A) {1, 2, 3, 4, 5, 6} (B) {(1, 3), (1, 4), (1, 6)} (C) {(2, 1), (6, 3), (2, 4)} (D) {(3, 2), (6, 4), (4, 1)} (E) None of the above.

Which of the following relations equals the relation {(a, b), (1, 2), (x, y)}? (A) {(a, b), (1, x), (2, y)} (B) {(x, y), (a, b), (1, 2)} (C) {(12, xy), (a, b)} (D) {(b, a), (2, 1), (x, y)} (E) None of the above.

What is the inverse of {(1, 2), (3, 6), (4, 2)}?

9.

The inverse of which of the following is a function? (A) {(1, 1) (1, 2), (1, 3)} (B) {(a, 0), (b, 0), (c, 0)} (C) {(a, j ), (r, j), (a, r)} (D) {(1, 2), (2, 3), (3, 2)} (E) {(u, v), (w, v), (y, x)}

10. What is the range of the inverse of {(P, Q), (R, S),

(T, V )}? (A) {1, 2, 3} (B) {P, Q, R} (C) {Q, S, V} (D) {P, R, T} (E) {P, Q, R, S, T, V}

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(D) A set is a relation if all its elements are ordered pairs; I and III meet this condition; II does not. (806)

2.

(B) Two relations are equal if their elements are equal. Though it doesn’t matter in what order the ordered pairs are listed, if the elements of the ordered pairs are switched the relation is changed. (806)

3.

(E) The range of a relation is the set of second elements of the ordered pairs. The range of {(1, 2), (3, 4), (5, 6)} is {2, 4, 6}. (806)

4.

(A) The domain is the set of first elements of the ordered pairs. The domain of {(1, 2), (2, 1), (1, 5)} is {1, 2}. (806)

5.

(A) To be a function, a relation must not repeat any of the first elements of its ordered pairs. The first elements of {(1, 1), (2, 2), (3, 3)} are all distinct. (806)

6.

(C) To find the inverse simply reverse all the ordered pairs. (807)

7.

(C) Reversing (1, 2) we get (2, 1); reversing (3, 3) we get (3, 3); reversing (2, 1) we get (1, 2). Though they are in a different order, the ordered pairs of the inverse of (3) are the same as the ordered pairs of (3). (807)

8.

(B) The domain of the inverse is the range of the relation, or {1, 3, 5}. (806, 807)

9.

(A) If the inverse of the relation is to be a function, the second elements must be all distinct. The second elements of the ordered pairs of (1) are 1, 2, and 3, all distinct. (806, 807)

10. (D) The range of the inverse is the domain of the

function, or {P, R, T}.

(806, 807)

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Solution Sets Test Find the solution sets in Questions 1–3. 1.

3.

Find the solution sets in the positive integers for Questions 4–7. x79 (A) {7} (B) {9} (C) {16} (D) {2} (E) {9, 7} 5.

x 3 4 (A) {3} (B) {4} (C) {1} (D) {1} (E)

(x 1)(x 4) 0 (A) {4} (B) {1, 4} (C) {1, 1, 4} (D) {0} (E) {4}

Find the solution set in the negative integers for Questions 8–10.

(x 2)(x 1) 0 (A) {1} (B) {2, 1} (C) {1} (D) {2, 1} (E) {2, 1}

4.

7.

x93x (A) {3} (B) {9} (C) {3} (D) {3, 9} (E)

x 2x 4 (A) {1} (B) {2, 3} (C) {1, 2, 3} (D) {1, 2, 3, 4} (E)

2x 4 0 (A) {2} (B) {4} (C) {4} (D) {0} (E) {2, 4}

2.

6.

8.

(x 3)(x 6) 0 (A) {3, 6} (B) {3, 6} (C) {3} (D) {6} (E)

9.

(2x 7)(x 3) 0 (A) {2, 7, 3} (B) {3} (C) {31⁄ 2} (D) {2} (E)

10. 10 2x 0

(A) {1, 2} (B) {10, 8, 6} (C) {1, 2, 3, 4, 5} (D) {1, 2, 3, 4} (E) {1, 2, 3, 4}

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(A) 2x 4 0. x 2, so the solution set is {2}. (808)

6.

(C) x 2x 4, or x 4. The positive integers less than 4 are 1, 2, and 3. (808)

2.

(A) x 9 3 x. 2x 6 or x 3. The solution set is {3}. (808)

7.

(A) (x 1)(x 4) 0. x 1 or 4. 4 is a positive integer but 1 is not, so the solution set is {4}. (808)

3.

(D) (x 2)(x 1) 0, so x 2 or 1. The solution set is {2, 1}. (808)

8.

(B) (x 3)(x 6) 0. x 3 or 6, both of which are negative integers, so the solution set is {3, 6}. (808)

9.

(E) (2x 7)(x 3) 0. x 31⁄ 2 or 3, neither of which is a negative integer. The solution set is . (808)

4.

5.

(D) x 7 9 or x 2 which is a positive integer. The solution set is {2}. (808) (E) x 3 4, or x 1, which is not a positive integer. The solution set is . (808)

10. (D) 10 2x 0. 2x 10 or x 5. The negative

integers greater than 5 are 1, 2, 3, and 4. (808)

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Axioms Test Use the following axioms to answer Questions 1–5. I. Commutative axiom for addition: a b b a II. Associative axiom for addition: a (b c) (a b) c III. Commutative axiom for multiplication: ab ba IV. Associative axiom for multiplication: (ab)c a(bc) V. Distributive axiom: a(b c) ab ac

In Questions 1–4, which axiom can be used to justify the given statements? 1.

5.

(3 7) 4 3 (7 4) (A) (B) (C) (D) (E)

3.

I II III IV V

3(6 2) 18 6 (A) (B) (C) (D) (E)

3 ⋅ 55 ⋅ 3 (A) (B) (C) (D) (E)

2.

4.

Which two axioms can be used to justify the following: 5(3 4) 20 15? (A) (B) (C) (D) (E)

I II III IV V

I II III IV V

I and II I and III III and V IV and V V and I

(2 ⋅ 5) ⋅ 3 (5 ⋅ 2) ⋅ 3 (A) (B) (C) (D) (E)

I II III IV V


(C) To go from 3 ⋅ 5 to 5 ⋅ 3 we switch the order of multiplication. The axiom that deals with order of multiplication is the commutative axiom for multiplication. (809)

2.

(B) Switching parentheses in addition involves the associative axiom for addition, II. (809)

3.

(C) To go from (2 ⋅ 5) ⋅ 3 to (5 ⋅ 2) ⋅ 3 we switch the order of multiplying inside the parentheses. This is justified by III. (809)

4.

(E) To go from 3(6 2) to 3 ⋅ 6 3 ⋅ 2 or 18 16, we use the distributive axiom. (809)

5.

(E) To go from 5(3 4) to 5 ⋅ 3 5 ⋅ 4 or 15 20 we use the distributive axiom. To go from 15 20 to 20 15 we use the commutative axiom of addition. (809)

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PA R T 7

VOCABULARY BUILDING THAT IS GUARANTEED TO RAISE YOUR SAT SCORE

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348 • VOCABULARY BUILDING THAT IS GUARANTEED TO RAISE YOUR SAT SCORE

Knowing Word Meanings Is Essential for a Higher SAT Score

Improving your vocabulary is essential if you want to get a high score on the Critical Reading Section of the SAT. We shall explain why this is so. The Critical Reading Section part of the SAT consists of two different question types: Sentence Completions and Reading Comprehension. Almost all SAT exam takers come across many “tough” words in this part, whose meanings they do not know. These students, thereby, lose many, many points because if they do not know the meanings of the words in the questions, they aren’t able to answer the questions confidently—and so, they are likely to answer incorrectly. Every correct answer on the SAT gives you approximately 10 points. The 19 Sentence Completion questions contain quite a number of “tough” words whose meanings you will have to know in order to answer these questions correctly. We must also bring to your attention the fact that several “tough” words show up in the Reading Comprehension passages of every SAT exam. Knowing the meanings of these difficult words will, of course, help you to understand the passages better. It follows that knowing what the passages are all about will give you many more correct answers for the Reading Comprehension questions that appear in the SAT—and each correct answer nets you approximately 10 points.

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VOCABULARY BUILDING THAT IS GUARANTEED TO RAISE YOUR SAT SCORE • 349

8 Steps to Word Power

1.

Study vocabulary lists. You have in this book just the list you need for SAT preparation. The SAT 3,400 Word List begins on page 363.

2.

Take vocabulary tests. “100 Tests to Strengthen Your Vocabulary” begins on page 415.

3.

Learn those Latin and Greek roots, prefixes, and suffixes that make up many English words. It has been estimated that more than half of all English words come from Latin and Greek. “Word Building with Roots, Prefixes, and Suffixes” begins on page 352.

4.

Have a college-level dictionary at home. Carry a pocket dictionary when you are moving about. Refer to a dictionary whenever you are not sure of the meaning of a word.

5.

Read—read—read. By reading a great deal, you will encounter new and valuable words. You will learn the meanings of many of these words by context—that is, you will perceive a clear connection between a new word and the words that surround that word. In this way, you will learn the meaning of that new word.

6.

Listen to what is worthwhile listening to. Listen to good radio and TV programs. Listen to people who speak well. Go to selected movies and plays. Just as you will increase your vocabulary by reading widely, you will increase your vocabulary by listening to English that is spoken well.

7.

Play word games like crossword puzzles, anagrams, and Scrabble.

8.

Make sure you learn the Vocabulary Strategies beginning on page 148.

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No One Can Dispute This Fact!

You will pile up SAT points by taking advantage of the valuable Vocabulary Building study and practice materials that are offered to you in the following pages of this chapter.

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You Don’t Have to Learn the Meaning of Every Word in the SAT 3,400 Word List

Go as far into the alphabetized groups as time permits. Use the Vocabulary Learning Steps listed on page 363. If you cannot learn the meanings of all the words in the 3,400 Word List, don’t fret. Whatever words you have added to your vocabulary before you take the actual test will raise your SAT Verbal score substantially. IMPORTANT NOTE: If you cannot spend time memorizing some of the words in the Gruber 3,400 Word List, I strongly suggest that you read through the Vocabulary Strategies in the Critical Thinking Strategies section beginning on page 59. Also make sure you study the roots and prefixes on pages 353 through 356, especially the checked ones. You may also want to study the Hot Prefixes and Roots in Appendix A.

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The Gruber Prefix-Root-Suffix List That Gives You the Meanings of Over 150,000 Words

Word Building with Roots, Prefixes, and Suffixes According to some linguistic studies, approximately 60 percent of our English words are derived from Latin and Greek. One reliable study has shown that a selected list of 20 prefixes and 14 root elements pertain to more than 100,000 words in an unabridged dictionary. Here we have done even better—we’ve given you a list of prefixes and roots which will give you meanings of over 150,000 words! The following entries of Latin and Greek roots, prefixes, and suffixes frequently show up in some of the words in the SAT Verbal areas, Sentence Completions, and Reading Comprehension. Learn these Latin and Greek word parts to increase your vocabulary immensely—and thus score well in the Verbal part of your SAT. The shortest and best way of learning a language is to know the roots of it; that is, those original primitive words from which other words are formed. —Lord Chesterfield

Lord Chesterfield is, in effect, saying that roots are used as important “building blocks” of many of our English words. As you study the following list of Latin and Greek roots, prefixes, and suffixes, have a dictionary by your side. Look up the meanings of the word examples that are given if you do not know their meanings.

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Roots A ROOT IS THE BASIC ELEMENT—FUNDAMENTAL OR ESSENTIAL PART—OF A WORD. The roots checked are especially important.

MEANING AND EXAMPLE*

ROOT ⻫ ag, act

field; as agriculture, agoraphobia

agr alt

do, act; as agent, counteract

high; as altitude, altar other; as altercation, alternative

alter ⻫ am

friend, love; as amity, amorous year; as annuity, annual

anim

man; as philanthropy, anthropoid

anthrop aper

open; as aperture, aperient

ROOT

MEANING AND EXAMPLE

clud, clus

close, shut; as conclude, recluse

cogn

know; as incognito, cognizant

cord

heart; as cordial, accord

corp

body; as corpulent, corpse world; as cosmic, cosmopolitan

cosm ⻫ cred

believe; as incredible, credentials

⻫ curr, curs

run; as current, cursory

ten; as decimal, decade

dec

apt

fit; as adapt, aptitude

dem

people; as democracy, demographic

aqu

water; as aqueous, aquacade

derm

skin; as epidermis, dermatologist

arch

rule, govern; as anarchy, matriarch star; as asteroid, disaster, astronomy

aster, astr

di

day; as diary, sundial

⻫ dic, dict

aud

hear; as audible, audition

dign

aur

gold; as auriferous

domin

low; as debase, basement

dorm

⻫ bas

speak, say; as indicate, contradict worthy; as dignity, indignant lord, master; as dominate, indomitable sleep; as dormant, dormitory

⻫ duc, duct

bell

war; as bellicose, antebellum

ben

good, well; as benevolent, benefactor

ego

I; as egotism, egomaniac

bibl

book; as biblical, bibliography

equ

equal; as equity, equanimity

bio brev

life; as biology, biopsy short; as brevity, abbreviation fall; as cadence, casualty, incident

cad, cas, cid cand

white, shining; as candid, candidate

⻫ cap, capt, cept intercept

take, hold; as capable, captive,

capit

head; as capital, decapitate

carn

flesh; as carnal, carnivorous

⻫ ced, cess celer cent chrom chron cid, cis clin ⴱ

yield, go; as cede, procession

swift; as celerity, accelerate hundred; as century, centipede color; as chromium, chromatic time; as chronology, chronic cut, kill; as suicide, precision lean, bend; as inclination, recline

Refer to a dictionary for word meanings you don’t know.

lead; as induce, ductile

⻫ fac, fact, fect, fic infection, fiction ⻫ fer

make, do; as facile, factory,

bear, carry; as fertile, confer

fid

faith, trust; as confide, infidelity

fin

end; as infinite, final

flect, flex form ⻫ fort

bend; as reflect, flexible

shape; as conform, reformation strong; as fortitude, fortify

frag, fract

break; as fragile, fracture

fug

flee; as fugitive, refugee

fus

pour; as confuse, fusion

⻫ gen gest

kind, race, birth; as generate, generic, generation carry, bring; as congestion, gestation

grad, gress

step, go; as graduate, digress

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MEANING AND EXAMPLE

ROOT

write; as autograph, graphic

graph

pleasing; as gratitude, congratulate

grat

water; as dehydrated, hydrant

hydr

entire, whole; as integrate, integral

integr ⻫ ject

throw; as inject, projection join; as conjunction, juncture

junct lat

carry; as translation, dilate

leg, lig, lect

free; as liberate, libertine

liber ⻫ loc log

speak, talk; as loquacious, circumloculight; as translucent, illuminate

great; as magnitude, magnificent hand; as manufacture, manual sea; as marine, maritime

large; as megaton, megaphone

ment

mind; as mentality, mentally

merg

plunge, sink; as submerge, merger

meter

measure; as chronometer, symmetry

micro

small; as microscope, microfilm

migr

wander; as migrate, immigration look; as admire, mirror

⻫ mit, miss

⻫ nat

send; as admit, submission

advise, remind; as admonish, monument death; as immortality, mortal

mot, mov

⻫ mut

drive; as compel, expulsion

pel, puls

hang; as pendant, pension

pend, pens pet

seek; as impetus, petition

petr

stone, rock; as petrify

phil

loving; as philosophy

sound; as phonic, phonetics

mega

⻫ mult

child; as pediatrics, pedagogue

phon

mother; as maternal, matrimony

⻫ mort

ped

fear; as claustrophobia

mater

mon

foot; as impede, biped, tripod

ped, pod

phob

magn

mir

father; as paternal, patriot

pater, patri

word, study; as catalogue, psychology

luc, lum

mar

work; as cooperation, operate

oper

place; as dislocate, local

loqu, locut tion

⻫ man

choose, gather; as legible, eligible, collect

MEANING AND EXAMPLE

ROOT

move; as motor, motility, movable

many; as multitude, multifarious change; as mutation, transmute, immutable

⻫ plic

fold, bend; as complicate, implicate

⻫ pon, pos ⻫ port pot

place, put; as component, compose

carry, bring; as porter, import drink; as potion, potable powerful; as potentate, impotent

poten

take, grasp; as apprehend, com-

prehend, prehens prehension

first; as protagonist, prototype

prot

mind; as psychological, psychic

psych

quer, quir, quis, ques inquisition, quest

ask, seek; as query, inquiry,

rule, govern; as regent, rigid, correc-

reg, rig, rect tive

laugh; as ridiculous, risible

rid, ris rupt

break; as rupture, erupt, interruption

sacr

holy; as sacred, sacrificial holy; as sanction, sanctify

sanct

know; as science, conscious, omniscient

sci, scio

watch; as periscope, horoscope

scop

⻫ scrib, script

write; as describe, prescription cut; as secant, bisect

born; as natal, innate

sec, sect

nav

ship; as naval, navigate

sed, sid, sess

neg

deny; as negate, renege

sent, sens

feel, think; as sentiment, sensible

⻫ sequ, secut

follow; as sequel, consecutive

nomen nov ocul

name; as nominee, nomenclature, cognomen new; as novelty, novice, innovation eye; as oculist, binocular

sit, seat; as sedate, reside, session

ser v

keep; as reserve, conservation

sist

place, stand; as assist, resistance

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MEANING AND EXAMPLE

ROOT

loosen; as dissolve, absolution

solv, solu

sleep; as somnambulist, insomnia

⻫ tract

soph

wisdom; as sophisticated, philosophy

trit

look, appear; as specimen, pros-

⻫ stat, stab

stand; as status, stability

string, strict

bind; as stringent, stricture

stru, struct

build; as construe, destructive

sum, sumpt

take; as assume, presumption

tang, ting, tact, tig contact, contiguous

touch; as tangent, contingency,

cover; as tegument, detect

teg, tect

distance; as telescope, teletype

tele

time; as temporary, extemporaneous

tempor ⻫ ten, tain

hold, reach; as tenant, tension, retain end; as terminal, terminate

term

land, earth; as inter, terrace

ter, terr

heat; as thermometer, thermos

therm

draw; as attract, extract rub; as trite, attrition thrust; as intrude, abstruse

trud, trus

shade; as umbrella, umbrage

umbra

breathe; as conspire, respiration

spir

twist; as contort, torsion

tort, tors

somn

⻫ spec, spect, spic pect, conspicuous

MEANING AND EXAMPLE

ROOT

urb

city; as suburb, urban

vac

empty; as vacate, evacuation

vad, vas

go; as evade, evasive

val, vail

be strong; as valid, prevail

⻫ ven, vent ⻫ ver

come; as convene, prevention

true; as veracity, aver word; as verbose, verbatim

verb

⻫ vert, vers

turn; as convert, reverse see; as evident, visible

vid, vis

conquer; as invincible, evict

vinc, vict

live; as vivacity, vital

viv, vit

call; as in vocation, revoke

voc, vok volv, volut

roll, turn; as in involve, revolution

Prefixes A PREFIX IS PART OF A WORD THAT MAY BE PLACED BEFORE THE BASIC ELEMENT (ROOT) OF A WORD.

The prefixes checked are especially important.

PREFIX

MEANING AND EXAMPLE

⻫ a, ab, abs

from, away; as avert, abjure, absent

⻫ ad to; as adhere. By assimilation, ad takes the forms of a, ac, af, al, an, ap, as, at; as aspire, accord, affect, allude, annex, appeal, assume, attract ambi, amphi amphibious ⻫ ante, anti

around, both; as ambidextrous,

before; as antedate, anticipate

MEANING AND EXAMPLE

PREFIX

⻫ contra, contro, counter controvert, counteract

⻫ de down, away from, about; as descend, depart, describe half; as demigod, demitasse

demi dia

across, through; as diameter, diastole

against; as antidote, antislavery

⻫ dis, di, dif fident

arch

first, chief; as archangel, archenemy

⻫ equi

auto

self; as autobiography, automatic

⻫ ex, e, ef

⻫ anti

good, well; as benediction, benefactor

ben ⻫ bi

two; as bilateral, bisect

⻫ circum

around; as circumnavigate, circumvent

⻫ com, con, col, cor, co together; as commit, concord, collect, correct, co-worker

against; as contradict,

apart, not; as dissension, division, dif-

equal; as equinox, equivalent out of, from; as extract, eject, efface

extra out of, beyond; as extraordinary, extraterrestrial ⻫ hyper

too much; as hypercritical, hypersensitive

hypo

too little, under; as hypochondriac, hypodermic

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MEANING AND EXAMPLE

PREFIX

⻫ in, il, im, ir into, in, on; as invade, illustrate, immerse, irritate ⻫ in, il, im, ir irresponsible

not; as indistinct, illegal, impossible, between, among; as interpose, introduce

inter, intro ⻫ mal, mis

bad; as malevolent, mistreat one, single; as monotone, monorail

mono neo

⻫ pre

before; as predict, precursory

⻫ pro

forward, before; as proceed, provide

⻫ re

back, again; as recur, recede backward; as retrogress, retrospect

retro

apart, away; as seduce, sedition

se

half; as semicircle, semiconscious

semi

new; as neoplasm, neophyte

⻫ sub

not; as nonentity, nonconformist

⻫ super

⻫ non

⻫ ob, of, op ⻫ omni

against; as obviate, offend, oppose

all; as omniscient, omnipresent straight; as orthodox, orthopedic

ortho

MEANING AND EXAMPLE

PREFIX

under; as submarine, subversive above, beyond; as superpose, supernatural

syn, sym with, at the same time; as synonymous, sympathetic ⻫ trans

across; as transcontinental, transmit

ultra

beyond; as ultraliberal, ultramodern

all; as pantheism, Pan-American

⻫ un

not; as unaware, uninformed

⻫ peri

around; as perimeter, periscope

⻫ uni

one; as unanimous, uniform

⻫ poly

many; as polygon, polygamy

⻫ post

after; as postpone, postmortem

pan

instead of; as vice-chancellor, viceroy

vice

Suffixes A SUFFIX IS PART OF A WORD THAT MAY FOLLOW THE BASIC ELEMENT (ROOT) OF A WORD. The suffixes checked are especially important.

MEANING AND EXAMPLE

SUFFIX ⻫ able

able; as pliable, returnable

acious, cious meretricious

belonging to; as legal, regal

⻫ ance, ence ⻫ ate

state of; as abundance, indulgence

one who; as candidate, advocate

ary, eer, er one who, concerning; as secretary, engineer, mariner ⻫ cy

state, position of; as adequacy, presidency

dom ⻫ ence

⻫ escent ⻫ fy

capable of being; as evil, servile

⻫ ion

act of; as desperation, perspiration characterized by; as spacious, illustrious

⻫ ish

like; as boyish, foolish belief in or practice of; as idealism, capitalism

ism

ist one who practices or is devoted to; as anarchist, harpist ⻫ ive

relating to; as abusive, plaintive

⻫ ness

quality of; as willingness, shrewdness

or, er

state of; as presence, credence

or y

becoming; as adolescent, putrescent

make; as beautify, sanctify

state of; as harmony, matrimony

mony

state of; as freedom, serfdom

one who; as player, actor

er, or

⻫ il, ile ⻫ ious

act, condition; as courage, foliage

age al

having the quality of; as capacious,

MEANING AND EXAMPLE

SUFFIX

one who; as monitor, employer a place for; as factory, depository

⻫ ous, ose

full of; as ponderous, verbose

ship

state of, skill; as friendship, gamesmanship

⻫ some

characteristic of; as loathsome, fearsome

hood

state of; as knighthood, childhood

tude

state of; as lassitude, rectitude

ic, id

of, like; as bucolic, acrid

ward

in the direction of; as windward, backward

⻫y

full of; as unruly, showy

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A List of SAT Words Appearing More Than Once on Actual SAT Exams

We have made a computerized analysis of frequently occurring words on 47 complete SAT exams. (1,175 questions have been examined.) Following is a list of 132 SAT words appearing more than once on these 47 actual SAT exams. The definitions of these words have not been included here because we want you to refer to a dictionary to learn the meanings of these words, which have been repeated in subsequent SAT question sections. Note that after each word a numeral indicates the number of times that the word has appeared on the 47 actual SAT exams. Also note that certain pairs of words have a left-side bracket. The bracket indicates that the words are very closely allied in meaning—so if you learn the meaning of one of the two words in the pair, you will easily arrive at the meaning of the other word of the pair. Learn the meanings of these words, as they have a tendency to be repeated in questions of the SAT.

abolish 2 abridge 2 abstemious accent 1 accented 1 accolade 2 acquiesce 2 affirmation 2 amass 2 ambivalence 1 ambivalent 1 ambulator y 2 ameliorate 2 amity 2 anchor 2 antediluvian 2 ascendancy 2 atrophy 2 bane 1 baneful 1 bizarre 2 blunder 2 bungle 2 burgeon 2 capitulate 1 capitulation 1 capricious 4 clemency 2

2 coalesce coalescence 1 1 cohere coherent 1 1 compress compression 1 1 confide confidential 1

confound 2 congeal 2 contaminant 1 contaminate 2 converge 2 convivial 2 copious 2 corroborate 2 corrugated 2 corrupt 1 corruption 1 cursor y 2 daunt 3 dauntless 1 debilitate 2 deplete 2 discrepancy 3 disentangle 2 disputatious 1 dispute 2

1 distend distention 1

drawback 2 efface 3 effer vesce 1 effer vescent 1 enhance 2 enigmatic 2 ephemeral 3 equilibrium 3 euphonious 1 euphony 1 evacuate 2 evanescent 2 expedite 1 expeditious 1 expendable 1 expenditures 1 exclude 2 facilitate 2 fallow 2 fertile 2 flourish 3 flower 1 fraudulent 3 fruitful 1 fruitless 1 garner 2

guile 2 hackneyed 2 hefty 2 hideous 2 hilarity 2 humane 2 hypocrisy 1 hypocritical 1 innocuous 2 irascible 2 jettison 2 kindle 2 leniency 1 lenient 1 levity 1 levitate 1 listless 2 maladroit 2 mitigate 2 mobile 2 munificent 2 munificence 1 myriad 2 nefarious 2 obscure 1 obscurity 1 opaque 1 opacity 1

parsimony 2 paucity 2 penur y 2 peripheral 2 peripher y 2 placate 2 precise 1 precision 1 premature 2 premeditated 2 prevalent 2 proclivity 2 prodigal 1 prodigious 2 profuse 1 profusion 2 pulverize 1 pulverized 1 rant 2 recalcitrant 2 recant 2 replete 2 rescind 2 reser ve 2 ruffle 2 rupture 2 saccharine 2 salubrious 2

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somber 4 specify 1 specificity 1 spurn 2 squander 2 stymie 2

subtle 2 summar y 2 summon 3 sumptuous 2 surreptitious 1 surreptitiously 1

tantamount 2 tenacious 1 tenacity 1 transience 1 transient 1

turbulence 3 venturesome 3 viable 2 vibrancy 1 vibrant 1

vilification 2 virulence 1 virulent 1 whet 2 zany 2

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The 291 Most Important/Frequently Used SAT Words and Their Opposites

Following is a list of popular SAT words and their opposites. Note: These words fit into specific categories, and it may be a little easier memorizing the meaning of these important words knowing what category they fit into. POSITIVE

NEGATIVE

POSITIVE

NEGATIVE

TO PRAISE

TO BELITTLE

acclaim applaud commend eulogize exalt extol flatter hail laud panegyrize resound tout

admonish assail berate calumniate castigate censure chastise chide decry denigrate denounce disparage excoriate execrate flay lambaste malign reprimand reproach scold upbraid vilify

TO CALM OR MAKE BETTER

TO MAKE WORSE OR RUFFLE

abate accede accommodate allay ameliorate appease assuage comply concede conciliate gratify mitigate mollify pacify palliate placate propitiate quell satiate

alienate antagonize contradict dispute fend off embitter estrange incense infuriate nettle oppugn oppose rebuff repel repulse snub

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POSITIVE

NEGATIVE

POSITIVE

NEGATIVE

PLEASANT

UNPLEASANT

YIELDING

NOT YIELDING

affable amiable agreeable captivating congenial cordial courteous decorous engaging gracious obliging sportive unblemished undefiled

callous cantankerous captious churlish contentious gruff irascible ireful obstinate ornery peevish perverse petulant querulous testy vexing wayward

accommodating amenable compliant deferential docile flexible hospitable inclined malleable obliging pliant submissive subservient tractable

adamant determinate immutable indomitable inflexible intractable intransigent recalcitrant relentless resolute steadfast tenacious

GENEROUS

CHEAP

COURAGEOUS

TIMID

altruistic beneficent benevolent charitable effusive hospitable humanitarian magnanimous munificent philanthropic

frugal miserly niggardly paltry parsimonious penurious provident skinflinty spartan tight-fisted thrifty

audacious dauntless gallant intrepid stalwart undaunted valiant valorous

diffident indisposed laconic reserved reticent subdued timorous

SCARCE OR POOR

LIVELY

BLEAK

dearth deficit destitute exiguous impecunious impoverished indigent insolvent meager paltry paucity penurious scanty scarcity sparse

brisk dynamic ebullient exhilaration exuberant inspiring provocative scintillating stimulating titillating

dejected forlorn lackluster lugubrious melancholy muted prostrate somber tenebrous

ABUNDANT OR RICH affluent bounteous copious luxuriant multifarious multitudinous myriad opulent pecunious plenteous plentiful plethoric profuse prosperous superabundant teeming wealthy

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POSITIVE

NEGATIVE

CAREFUL

CARELESS

HAUGHTY

HUMBLE

chary circumspect conscientious discreet exacting fastidious gingerly heedful judicious meticulous provident prudent punctilious scrupulous scrutiny wary

culpable felonious indifferent insouciant lackadaisical lax negligent perfunctory rash remiss reprehensible temerarious

affected aristocratic arrogant audacious authoritarian autocratic condescending disdainful egotistical flagrant flippant imperious impertinent impudent insolent ostentatious pompous proud supercilious vainglorious

demure diffident indisposed introverted laconic plebian reluctant restrained reticent subdued subservient taciturn timid timorous unassuming unostentatious unpretentious

Note: In many cases you can put a prefix “im” or “un” in front of the word and change its meaning to an opposite. EXAMPLE: Pecunious. Opposite: Impecunious Ostentatious. Opposite: Unostentatious

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Practice Questions

Answers to Practice Questions

1. Example: Find OPPOSITE of EXTOL: (A) oppose (B) restrain (C) enter (D) deviate (E) denigrate 2. ALLAY (opposite): (A) incense (B) drive (C) berate (D) signify (E) determine 3. DECOROUS (opposite): (A) scanty (B) irascible (C) musty (D) pliant (E) rigid 4. AMENABLE (opposite): (A) tiresome (B) uncultured (D) soothing (E) careless

2. Choice A is correct. ALLAY fits into the category of TO CALM. Incense fits into the opposite category— TO MAKE WORSE or TO RUFFLE. 3. Choice B is correct. DECOROUS fits into the category of PLEASANT. The opposite category is UNPLEASANT. Irascible fits into this category. 4. Choice C is correct. AMENABLE fits into the category of YIELDING. Intransigent fits into the opposite category—NOT YIELDING.

(C) intransigent 5. Choice D is correct. MUNIFICENT fits into the category of GENEROUS. Penurious fits into the category of CHEAP, the opposite category.

5. MUNIFICENT (opposite): (A) simple (B) pallid (C) crafty (D) penurious (E) stable 6. PLETHORIC (opposite): (A) impecunious (B) slothful (D) reticent (E) sly

1. Choice E is correct. EXTOL fits into the category of TO PRAISE. Denigrate fits into the category TO BELITTLE—the opposite category.

(C) indifferent

6. Choice A is correct. PLETHORIC fits into the category of ABUNDANT or RICH. Impecunious fits into the opposite category of SCARCE or POOR. 7. Choice E is correct. METICULOUS fits into the category of CAREFUL. Perfunctory fits into the category of CARELESS (or mechanical).

7. METICULOUS (opposite): (A) timid (B) plenteous (C) peevish (D) intractible (E) perfunctory 8. IMPERIOUS (opposite): (A) unostentatious (B) lackadaisical (C) insolvent (D) churlish (E) immutable

8. Choice A is correct. IMPERIOUS fits into the category of HAUGHTY (high-brow). Unostentatious fits into the category of HUMBLE, the opposite category. 9. Choice B is correct. TIMOROUS fits into the category of TIMID. Intrepid fits into the opposite category of COURAGEOUS.

9. TIMOROUS (opposite): (A) judicious (B) intrepid (C) multifarious (D) benevolent (E) tenebrous 10.

LUGUBRIOUS (opposite): (A) flexible (B) unblemished (C) ebullient (D) concilatory (E) impertinent

10. Choice C is correct. LUGUBRIOUS fits into the category of BLEAK or dismal. Ebullient fits into the opposite category of LIVELY.

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The Gruber SAT 3,400 Word List

Every new word that you learn in this SAT word list can help you to add extra points to your SAT verbal score.

Vocabulary Learning Steps 1.

Conceal each definition with a card as you go down the column.

2. Jot down each word whose meaning you do not know. Then prepare a flash card for each word you did not know. Write the synonym (similar meaning) on the back of the card. 3.

Study the flash cards that you have made up.

4. After you have studied the DID-NOT-KNOW flash cards, give yourself a flash card test. Put aside the flash cards for the words you did know. 5. For each word you still do not know, write a sentence that includes the word you still have not learned well. 6. Now test yourself again on the DID-NOT-KNOW flash cards referred to in Step 5. Put aside your flash cards for the words you did know. 7.

Study the new reduced pile of DID-NOT-KNOW flash cards.

8.

Give yourself a flash card test on this new reduced DID-NOT-KNOW pile.

9. Keep reducing your DID-NOT-KNOW flash card pile until you have no DID-NOT-KNOW words. IMPORTANT Do not throw your flash cards away. Keep the cards for reinforcement testing in the future. In past exams, 70 to 80 percent of all test vocabular y words appeared on this list!

ABACK–AZURE

aback abandon

(preceded by taken) surprised; startled to leave; to give up; to discontinue

abate

to lessen; to decrease

abdicate

abase

to humiliate; to humble; to lower

abduct

abash

ashamed; embarrassed

aberration

to yield; to give up to take away; to kidnap abnormality; deviation

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abet

to aid; to encourage a temporary postponement

abeyance

to hate; to detest

abhor

abide (two meanings)

to remain; to put up with

upward slope

acclivity

honor; award; approval

accolade

to make fit; to help

accommodate

a partner in crime

accomplice

abject

miserable; wretched

accord

agreement

abjure

to give up (rights)

accost

to approach and speak to

a washing; cleansing

ablution abnegate

to deny; to reject

accredit

abolition

doing away with; putting an end to

accretion

to detest; to dislike strongly

abominate

original inhabitant

aborigine

unsuccessful

abortive

to be large in number

abound aboveboard

honest; frank; open

equipment; outfit

accoutrement

to approve; to certify an increase; an addition

accrue

to gather; to accumulate

acerbic

sharp or bitter in smell or taste a weakness

Achilles’ heel

to admit; to confess

acknowledge acme

highest point; peak

abrade

to wear away

acoustics

branch of physics dealing with sound

abridge

to shorten

acquiesce

to agree; to consent

abrogate

to abolish; to repeal

acquit

abscond

to leave secretly; to flee

acrid

absolve

to free from responsibility

abstemious drinking abstinence

moderate or sparing in eating or self-denial; resisting tempting foods

hard to understand ridiculous; unreasonable

absurd abut

to touch; to rest on or against wretched; extremely bad

abysmal abyss

a bottomless pit; anything infinite

academic (two meanings) pertaining to school; theoretical or unrealistic accede

to agree to

accelerate

to speed up; to move faster

accessible

easy to approach; open

access accessor y acclaim acclimate

bitter to the taste or smell; sarcastic

approach; admittance something additional to greet with approval to adapt; to get used to

harsh in speech or behavior

acrimonious

word formed from initials

acronym

fear of heights

acrophobia

abstract (two meanings) a summary (noun); to remove (verb) abstruse

to free of guilt; to clear

to put into motion or action

actuate

mental keenness; shrewdness

acumen acute

sharp; keen endlessly; forever

ad infinitum ad lib

to act or speak without preparation

adage

a familiar saying stubborn; unyielding

adamant adapt

to adjust; to change

addendum

something added as a supplement

addled

confused

adduce

to give an example in proving something

adept

highly skilled

adherent (two meanings) sticking fast (adjective); a follower or a supporter (noun) adipose

fatty

adjacent

near; close; adjoining

adjudicate

to judge

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a subordinate; an assistant

adjunct

to warn

admonish ado

fuss; trouble

adonis

a very handsome man

adorn

to dress up; to decorate

adroit

skillful; clever excessive praise or flattery

adulation

to make impure

adulterate

an arrival; a coming

advent

accidental; nonessential

adventitious

enemy; opponent

adversar y adversity

a misfortune; distress

advocate

to recommend; to defend a shield; protection; sponsorship

aegis

pertaining to beauty

aesthetic

friendly; agreeable

affable

a phony attitude; insincerity

affectation affiliate

to associate or to unite with

affinity

attraction to a statement that something is true

affirmation affix

to attach

affliction

great suffering; hardship

affluence

wealth an insult

affront

outcome; result

aftermath

open-mouthed; surprised

agape

a list or program of things to be done

agenda

to enlarge or to expand

aggrandize aggravate intensify

to worsen an already bad situation; to

aggregate

to collect; to gather together

aghast agile agitate

shocked; terrified able to move quickly to upset; to stir up one who doubts the existence of God

agnostic agoraphobia agrarian ague

fear of open places pertaining to farmers and agriculture

a fever; plague

liveliness; willingness

alacrity

(two meanings) a seabird; a constant

albatross burden

although

albeit

chemistry of the Middle Ages

alchemy alias

an assumed name

alien

strange; foreign to make others unfriendly to you

alienate

furnishing food or nourishment

alimentar y allay

to relieve or to calm so-called; supposed

alleged

a symbolic work of literature

allegor y

rapid; quick

allegro alleviate

to lessen; to relieve

allocate

to set aside for a specific purpose to hint at; to refer to indirectly

allude

tempting; fascinating; charming

alluring

alluvial pertaining to a deposit of sand formed by flowing water aloft

up in the air; high

aloof

reserved; cool; indifferent

alter

to change an argument; a disagreement

altercation

unselfishness; concern for others

altruism

to combine; to unite; to blend

amalgamate amass

to accumulate; to collect a big, strong, masculine woman

amazon

ambidextrous

equally skillful with either hand

surround; on all sides

ambient

unclear; open to more than one inter-

ambiguous pretation ambivalence or someone

conflicting feelings toward something pleasing to the taste or smell

ambrosial ambulator y

moving about; capable of walking

ambuscade

hidden or secret attack

ameliorate amenable amend

to improve; to make better agreeable; responsive to change; to alter

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courtesies; social graces; pleasantries

amenities

friendly; pleasant

amiable

friendly; agreeable

amicable

a lobby or waiting room

anteroom

song of praise

anthem

collection of literary works

anthology

amiss

wrong; faulty; improper

anthropoid

amity

friendship

anthropomorphic objects, gods, etc.

official pardon for an offense

amnesty

lacking a sense of right and wrong

amoral

amorphous

shapeless

amphibious

able to live on both land and water

roomy; abundant

ample amplify

to make larger or greater

amulet

a charm worn to keep evil away something out of place or time

anachronism

drug that relieves pain

analgesic

playful or silly act; prank

a remedy; a counteractive

antidote antipathy

intense dislike

antipodes

opposite sides (of the earth) ancient; extremely old

antiquated

an exact opposite

antithesis

indifference; lack of feeling

apathy

analogy

similarity or comparison

ape (two meanings) or to mimic (verb)

anarchy

absence of government

aperture

a curse; a person or thing to be avoided

anathema

apex

the highest point; summit

helping; subordinate

aphasia

anecdote

a short, entertaining story

aphorism

regarding; concerning great suffering or grief

anguish

without water

anhydrous animadversion

criticism; comment that opposes

to give life to

animate

hatred; hostility

animosity

hostile feeling

animus

apiar y

loss of the ability to speak brief saying; proverb place where bees are kept self-confidence; poise

aplomb apocr yphal

apoplexy

sudden loss of consciousness; paralysis

apostate

one who gives up his beliefs

apothecar y apothegm

anneal

to heat and then cool; to toughen

apotheosis God

specified income payable at stated intervals

annuity annul

to cancel; to do away with abnormal; inconsistent

anomalous anon anoxia

lack of oxygen that which goes before something else

antediluvian anterior

very old-fashioned; primitive

located in front or forward

glorification of a person to the rank of

to frighten; to cause loss of courage

apparel apparition appease

soon

antecedent

appall

druggist brief instructive saying

historical records

to totally destroy

doubtful; not authentic

farthest point away from the earth

apogee

annals

annihilate

a monkey (noun); to imitate

an opening; a gap

ancillar y

anent

attributing human form to

anticlimax something unimportant coming after something important

loving

amorous

antic

resembling man

appellation append apposite apprehend

clothing; attire a ghost to soothe; to satisfy a name to attach; to add appropriate (two meanings) to seize; to understand

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apprehensive

fearful; anxious

to inform

apprise

approbation

approval

appropriate (adjective)

to take possession of (verb); suitable

appurtenance something added to another more important thing apropos

relevant; appropriate; fitting

aptitude

ability pertaining to water

aquatic

like an eagle; curved or hooked

aquiline

rising

ascendant

to find out; to determine

ascertain ascetic fort

one who denies his body pleasure and com-

ascribe

to attribute; to credit as to a cause or source

aseptic

without bacteria

asinine

stupid; silly (preceded by to look)

askance ciously

sidewise; suspi-

crooked; out of position

askew

harshness; roughness

asperity

a damaging remark

arable

good for farming

aspersion

arbiter

a judge; an umpire

aspire

to desire; to have an ambition

partial; biased

assail

to attack; to assault

a shaded area

assay

to test; to try

arcane

mysterious

assent

archaic

out-dated; old-fashioned

assertive

arbitrar y arbor

study of remains of past cultures

archeology

original; first of its kind

archetype archipelago

group of islands public records and documents

archives

intensely enthusiastic

ardent

difficult; strenuous

arduous

to agree; to accept confident; positive to estimate the value of

assess

diligence; care

assiduity

to absorb

assimilate assuage

to calm; to make less severe

asteroid

a very small planet

astral

pertaining to the stars in the wrong direction

aria

a solo in an opera

astray

arid

dry

astringent substance that contracts blood vessels or shrinks tissues

armistice

a truce; suspension of hostilities

aromatic

pleasant-smelling to accuse

arraign arrant

notorious; downright

array

an orderly arrangement

arrears arrogant arroyo

(preceded by in) in debt proud; haughty a deep ditch caused by running water

arson

illegal burning of property

artful

cunning; tricky; crafty

articulate

to speak clearly

artifact

a handmade object

artifice

trick; deception

artisan

one skilled in arts and crafts

shrewd; very smart

astute asunder

into separate parts

asylum

a safe place; a refuge

atavistic ancestor

one who denies God’s existence

atheist atlas

book of maps

atone

to make up for; to repent cruel; brutal

atrocious

to waste away; to become useless

atrophy attenuated attest

going back to behavior found in a remote

decreased; weakened

to confirm; to declare to be correct

attribute (two meanings) to credit or assign to (verb); a characteristic or trait (noun)

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attrition

a wearing down or away; a decline

autonomy

self-rule

atypical

abnormal; not usual

autumnal

mature; declining

up-to-date; fully informed

au courant

boldness; daring

audacity

capable of being heard

audible

to examine accounts

audit

to predict

augur

aura

a radiance; a glow

rosy; pertaining to the dawn

auroral

reluctant; not willing

averse

intense dislike to prevent; to turn away

avert

place where birds are kept enthusiastic

avid

a hobby; not one’s regular work heaviness; weight

to declare openly

avow

severe; stern; self-disciplined

austere

to declare; to state firmly

avoirdupois

favorable

auspicious

to get even; to take revenge

avocation

approval; support

auspices

avenge

aviar y

pertaining to the sense of hearing

aural

greed

aversion

majestic; worthy of respect; impressive

august

avarice

aver

to increase; to make greater

augment

giving assistance; subordinate

auxiliar y

like an uncle

avuncular

authenticate

to confirm; to make acceptable

awe

authoritative

dictatorial; having power

awr y

autocratic

despotic; unlimited in authority

axiom

true statement; established principle

automaton

self-operating machine; robot

azure

blue

(in awe of ) great admiration for or fear of twisted to one side; in the wrong direction

BACCHANALIAN–BUTTRESS bacchanalian

wild with drunkenness

to nag; to annoy

badger badinage baffle bagatelle

balk balm

uncultured; crude

a poet

to confuse; to bewilder

bark

a boat or sailing vessel

thing of little value; trifle

harmful; menacing; pernicious to stop short something that calms or soothes

banal

common; ordinary; trite

bandy

to exchange (as words)

banter

barbarous bard

balmy (two meanings) mild and refreshing; mentally unstable (slang)

bane

a pointed part, as of an arrow or fishhook

playful, teasing talk

bait (two meanings) to entrap or to seduce (verb); a decoy (noun) baleful

barb

cause of ruin, harm, or distress teasing; good-natured joking

baroque

overdecorated; showy

barrage

heavy attack lawyer (British)

barrister bask

to lie in or be exposed to warmth

bastion

a strong defense; a fort

bauble

showy but useless thing; trinket

bawdy

indecent; humorously obscene

bayou

marshy body of water

beacon

a light used for warning or guiding

beatitude

state of bliss

bedlam up-roar

(two meanings)

a madhouse; a noisy

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to confuse; to perplex

befuddle

to produce

beget

to resent another’s success or enjoyment

begrudge

to deceive; to charm

beguile

huge animal

behemoth

obligate; indebted

beholden

delayed or detained

belated

to encircle (with an army); to annoy

beleaguer

to put down; to humiliate

belittle

warlike; quarrelsome

belligerent

to yell loudly

bellow

benediction

blessing one who helps or supports another

benefactor beneficiar y

one who receives benefits or profits

benevolent

generous; kindly harmless; gentle

benign benignant

kindly; gentle

bequeath

to hand down; to pass on to to scold severely

berate

a narrow-minded, prejudiced person

bigot

bad-tempered; cross

bilious bilk

to cheat; to swindle

binge

a spree; wild party

biped

two-legged animal temporary shelter

bivouac bizarre

weird; strange

blanch

to whiten; to make pale mild; tasteless; dull

bland

blandishment

flattery

bored with life; unexcited; indifferent

blasé

blasphemy disrespect for holy places, people, or things; irreverence blatant annoyingly conspicuous; offensively noisy and loud to display; to proclaim

blazon

unsheltered; gloomy

bleak

blurred; dimmed

blear y

destruction; withering; disease

blight

extreme happiness

bliss

bereave by force

to leave in a sad or lonely state; to deprive

berserk

frenzied; violently destructive

bludgeon

beseech

to beg; appeal to

blunt (two meanings) abrupt in speech or manner; having a dull edge

to attack

beset

to overwhelm; to close in on

besiege

to make dirty

besmirch bestial

savage; brutal

bestow

to give or present to mount (a horse)

bestride

engaged; pledged to marry

betrothed bevy

a large group to cast a spell on; to charm; to fascinate

bewitch bias

preference; prejudice

bibliophile bibulous bicker bide biennial

carefree; light-hearted

blithe

lover of books absorbent; fond of alcoholic beverages

to quarrel (one’s time) to wait for a favorable opportunity occurring every two years

a short, heavy club

(out) to utter suddenly or indiscreetly

blurt

to speak noisily; to boast

bluster

to indicate in advance, as an omen does

bode

bog (two meanings) a swamp (noun); to sink or become stuck in (verb) false; fake

bogus

to prop up; to support

bolster bolt

to dash out suddenly; to discontinue support of

bombastic language

witty remark

bon mot bona fide bondage

using impressive but meaningless

genuine; in good faith slavery

boon

a benefit; a blessing; a favor

boor

a rude or impolite person

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booty

stolen money or goods

bronchial

pertaining to the windpipe to bully; to intimidate

boreal

northern

browbeat

borne

carried; put up with

bruit

botch

to mess up; to perform clumsily

brunt

plentiful; abundant

bountiful

bourgeoisie

middle class

bowdlerize to censor; to remove offensive passages of a play, novel, etc. braggart

one who boasts

brandish

to shake or wave a weapon aggressively

brash

offensively bold; rude

brawn

muscular strength

brazen

shameless or impudent

breach

a violation; a gap

brevity

briefness

brigand

a robber

pertaining to the countryside; rural

buffoon

clown or fool

bugbear

something causing fear

bulbous

swollen; shaped like a bulb

bulwark

a strong defense conceited; arrogant

bumptious

to do things clumsily or badly

buoyant (two meanings) able to float; lighthearted and lively system of government through

bureaucracy departments

brothers

brethren

bucolic

buoy (two meanings) a floating object (noun); to encourage (verb)

width

breadth

a pirate

bungle

a show of courage; false bravery

bravado

abrupt in manner, blunt; rough

buccaneer

pertaining to cows or cattle

bovine

shock, force, or impact, as of a blow

brusque

reward; generosity

bounty

to spread the news

to flourish; to grow rapidly

burgeon

burlesque a speech or action that treats a serious subject with ridicule

brine

salt water

burly

brisk

lively; quick

burnish

to polish

buttress

any prop or support

showing irritation

bristling

muscular; husky

to introduce (a subject)

broach

a pamphlet

brochure

CABAL–CYNOSURE cabal

a small, secret group

calligraphy

cache

a hiding place

callous

unyielding; insensitive

callow

young and inexperienced

cacophony

harsh or unpleasant sound

cadaverous

pale; ghastly; corpselike

fancy handwriting

a false accusation; slander

calumny

cadence

rhythm; beat

camaraderie

caesura

pause

canard

a false story, report, or rumor

candor

honesty; openness; frankness

canine

pertaining to dogs

cajole

to coax; to persuade

calamitous caliber

causing trouble or misery; disastrous degree of worth

canny

loyalty; friendship

shrewd

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rule; law; standard

canon

cant insincere statements usually made in a singsong tone cantankerous

bad-tempered; quarrelsome

smooth, easy pace; gallop

canter

to make a survey

canvass

spacious; roomy

capitulate

to surrender

capricious

erratic; impulsive

captivate

to capture; to charm; to fascinate

carapace

shell; hard, protective covering causing cancer

principal; chief to swerve; to dip to one side an exaggerated portrayal

caricature

slaughter; massacre

carnage

sensual; sexual

carnal

flesh-eating

carnivorous

to engage in a noisy, drunken party

carouse

carp (two meanings) a type of fish (noun); to complain (verb)

carte blanche

cartographer

mapmaker

a waterfall

cascade caste

freedom to use one’s own judgment

association of business firms

cartel

a haughty and casually indifferent person

cavalier

a warning to quibble; to argue to leap about; to frolic speed; swiftness

celerity celestial

heavenly

celibate

unmarried

censure

to criticize sharply

centrifugal

moving away from the center

cerebration

thinking; using one’s brain

certitude

sureness; certainty

cessation

a stopping; a discontinuance

chafe

to irritate; to annoy

chaff

worthless matter embarrassment; complete loss of courage

chagrin

chameleon a lizard able to change its skin color; a changeable or fickle person

complete disorder

chaos charisma

great appeal or attraction

charlatan

a fake; a quack cemetery; tomb

charnel

chasm

a wide gap

chaste

pure; virtuous

cataclysm

a violent change

chastise

catacomb

underground burial place

chattel

catalyst

person or thing that speeds up a result

cataract (two meanings) mality of the eye catastrophe

(of ) careful; cautious

char y

to punish

casualty (two meanings) an accident; one who is hurt in an accident

catholic

a procession; a sequence of events

cavalcade

social class

castigate

cathartic

to burn

cauterize

champ (verb) to bite impatiently; to show impatience (to champ at the bit)

decaying flesh

carrion

sarcastic; severely critical; corrosive

cavort

hard to please; faultfinding

careen

caustic

cavil

captious

cardinal

a private meeting

caveat

capacious

carcinogenic

caucus

large waterfall; abnor-

disaster; calamity cleansing universal; wide-ranging

to punish; to purify slave

chauvinism fanatical devotion to one’s country, sex, religion, etc. angel; an innocent person

cherub chic

stylish; fashionable

chicaner y chide

trickery; deception

to scold

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imaginary; fantastic; unreal

chimerical

art of handwriting

chirography

courteous; courageous; loyal

chivalrous

coddle

to treat tenderly

coerce

to force

choleric

easily angered

coffer

chronic

long-lasting

cog

rude; ill-bred

churlish

person or thing of no value; zero

cipher

roundabout; indirect

circuitous

roundabout way of speaking

circumlocution

to encircle; to limit or confine

circumscribe

cautious; careful

circumspect

to surround or entrap; to go around or

circumvent bypass

cite to quote a passage, book, author, etc.; to refer to an example politeness

civility

having great insight; keenly perceptive

clair voyant

to climb with effort or difficulty

clamber

noise

clamor

secretive; private

clandestine

harsh ringing sound

clangor

to make clear

clarify

clear and shrill

clarion

claustrophobia

fear of enclosed spaces

cleave (two meanings) to split something apart; to stick or cling to something cleft

split; divided mercy; leniency

clemency

a trite or worn-out expression

cliché

customers

clientele climax

highest point

clime

climate; region a small, exclusive group

clique cloistered clout

secluded; confined

(colloquial) power; influence

cloven coadjutor

a strongbox a gear tooth; a minor part

cogent

divided; split assistant; helper

convincing

cogitate

to think; to consider carefully

cognate

related; relevant aware

cognizant

family name; last name

cognomen coherent

logically connected; consistent

cohesive

tending to stick

cohort

a fortress

citadel

to blend; to merge; to fuse

coalesce

colleague; associate; partner to occur simultaneously

coincide

to work together; to cooperate

collaborate

collage collection of various bits and pieces (usually artistic) collate

to put together in order

collateral

security for payment of a loan

colloquial

informal conversation

colloquy

collusion conspiracy; agreement to commit a wrongful act huge; enormous

colossal

eager to fight; argumentative

combative

capable of catching fire easily

combustible comely

attractive

commemorative

honoring; remembering

to begin

commence commendation

praise

commensurate

proportionate

commiserate

to express pity for

commodious

roomy; spacious

communal

shared; pertaining to a group of people

compact (two meanings) firmly packed (adjective); a treaty (noun) compassion compatible

pity; sympathy agreeable; harmonious

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to force

compel

brief summary

compendium compensator y

paying back; making up for

yielding; submissive

complicity

partnership in a wrongful act ingredients; elements calmness of mind or manner

composure

required

compulsor y compunction

uneasiness; remorse

to calculate; to estimate

compute concave

hollow; curved inward

concede

to admit; to grant

concentrate (two meanings) increase in strength or degree

agreement; doing the same as others

to think deeply; to

confused; amazed

confounded congeal

compliant

components

merging; flowing together

confluent conformity

(note spelling) to make whole; to

complement complete

a large and destructive fire

conflagration

self-satisfied

complacent

to seize by way of penalty

confiscate

to freeze solid; to thicken

congenial

friendly; agreeable

congenital

existing at birth

conglomerate

mass; cluster; corporation

congregate

to gather; to assemble

congruent

in agreement

coniferous

bearing cones ( pertaining to trees)

conjecture

to guess pertaining to marriage

conjugal

conjure to call upon or to command a devil or spirit to practice magic; cast a spell on

concentric

having a common center

connivance pretend ignorance of another’s wrongdoing; conspiracy

conception idea or plan

(two meanings) a beginning; original

connoisseur

concession

allowance; the act of yielding

connote to soothe the anger of; to win over

conciliate

brief and to the point

concise

secret meeting

conclave

to invent; to devise

concoct

accompanying; attending

concomitant

agreement; harmony

concord

a crowd; a wide street

concourse concur

to agree to lower oneself to an inferior’s level

condescend condign

deserved; suitable seasoning; spices

condiment

expression of sorrow

condolence condone

to excuse; to overlook

conducive

tending to or leading to

conduit pipe or tube through which fluid or electricity passes confidant configuration

a close, trusted friend shape; arrangement

an expert

to suggest or imply pertaining to marriage

connubial consanguinity

close relationship, usually by blood

consecrate

to make holy

consensus

general agreement, especially of opinion

console (two meanings) a musical panel or unit (noun); to comfort (verb) to combine; to make or become solid

consolidate

in agreement or harmony

consonant

consort (two meanings) to associate or join (verb) consternation constituents constraints

a husband or wife (noun);

sudden confusion; panic voters; supporters restrictions; limits

constrict

to shrink; to bind

construe

to analyze; to interpret

consummate contagious contaminant contemn

to complete (verb); perfect (adjective) likely to spread; infectious substance that pollutes or infects to regard with scorn or contempt

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contemporar y current

happening in the same time period;

contemptuous

scornful ready to argue; quarrelsome

contentious

contest (three meanings) a competitive game (noun); to dispute (verb); to compete (verb) contiguous

nearby; neighboring

contingent

possible to twist; to distort

contort

smuggled or stolen goods

contraband

opposite

contrar y

to go against; to oppose

contravene

an embarrassing occurrence

contretemps

sorrowful; penitent

contrite

controversial

debatable; questionable

contumacious

disobedient; obstinate

corporeal

pertaining to the body

corpulent

fat; fleshy

cortege

funereal procession; group of followers

cosmic

pertaining to the universe; vast

close circle of friends

coterie

countenance (two meanings) the face (noun); to permit, tolerate, or approve (verb)

counterpart

messenger

courier

covert

to come together; to assemble

conventional

ordinary; usual to come together; to meet in a point or line

converge

being familiar with

conversant

converse (two meanings) to talk to someone (verb); the opposite (noun) curving outward

convex

conveyance

a vehicle

to desire

covet

to tremble in fear

cower coy

shy; modest

cozen

to trick

crafty

sly; tricky

crass

stupid; unrefined

crave

to desire strongly

to call together

creed

plentiful; abundant

copious

flirtation

coquetr y cordial

friendly; courteous

cornucopia corollar y corona

horn of plenty; abundance inference; deduction; consequence

crown; bright circle

believable

credible

convoke

(with) to deal with; to contend with

belief; trust

credence

credulity

cope

cowardly

craven

sociable; friendly

twisted; coiled

an agreement; a contract hidden; secretive

convivial

convoluted

duplicate; copy

coup a brilliant move; a successful and sudden attack

a bruise

convene

to cancel an order

countermand

contusion

to recover from an illness

worldly-wise; universal

cosmopolitan

covenant

convalesce

wrinkled; ridged; furrowed

corrugated

rudeness

a riddle

eating away, as an acid

corrosive

contumely

conundrum

to strengthen; to confirm

corroborate

readiness to believe; gullibility a religious belief

crescendo

gradual increase in intensity or loudness

crestfallen

dejected; humbled

crevice cringe criterion

an opening; a crack to shrink back, as in fear measure of value; standard of judging

crone

hag; withered old woman

crony

close friend

crotchety

grouchy; eccentric

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extremely important; decisive

crucial

a severe test or trial

crucible

to settle; to take on a definite form

cr ystallize cubicle

small compartment

cudgel

club; thick stick

style of cooking

cull

cursive

running or flowing

cursor y

superficial; hasty

cynic

to select; to pick to result in; to reach the highest point

culminate

to try to win favor by flattery

to cut short

curtail

pertaining to cooking

culinar y

to control; to check

curr y

a hint; a signal

cuisine

greed

cupidity curb

heavy; hard to handle because of size collected; accumulated

cumulative

mysterious; secretive

cr yptic

cue

cumbersome or weight

the essential part

crux

blameworthy

culpable

one who is critical; a fault-finder center of attention

cynosure

DAIS–DYSPHASIA

dais

platform; speaker’s stand

deciduous

dale

valley

decipher

dally

to waste time

declaim

to speak dramatically

dank

chilly and wet

declivity

downward slope

spotted

dappled

sneaking and cowardly; shameful

dastardly daub

to smear; to cover over with paint, etc.

daunt

to discourage to waste time; to idle

dawdle

in fact; in reality

de facto

a standstill; a tie

deadlock

a scarcity or lack

dearth

a complete failure; total collapse

debacle

to lower in rank; to humiliate

debase

to corrupt

debauch

decode; figure out the meaning of

decompose

decoy a person or thing that entices or lures, as into danger broken down by age or disease

decrepit

to speak out against

decr y

to reason out; to infer

deduce deem

to think; to believe; to judge to misuse funds; to embezzle

defalcate

defamator y damaging another’s reputation with false remarks

to weaken

default

debonair

pleasant; courteous; charming

defection

to fail to pay a debt or to perform a task desertion to postpone; to put off

debris

fragments; litter; rubble

defer

debut

first public appearance

deference

decant

moral deterioration to pour off (a liquid)

to decay; to break up into parts appropriate social behavior

decorum

debilitate

decadence

not permanent; passing

defile definitive

decapitate

to behead

deflect

decelerate

to slow down

defoliate

respect

to pollute; to corrupt comprehensive; complete to turn aside; to bend to strip of leaves

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to pay the cost of

defray deft

skillful

deploy

to place troops in position

depose

to remove from office

defunct

no longer in existence; extinct

depraved

sinful; immoral

degrade

to lower in degree or quality

deprecate

to disapprove of

deify

to idolize; to make god-like

deign

to lower oneself before an inferior delicious; very pleasing

delectable

to leave out; to cross out

delete

harmful

deleterious

to describe; to depict

delineate

delirium condition of mental disturbance; wild excitement delude

to deceive; to mislead

deluge

a flood; a rush

delve

to search; to investigate a popular leader who appeals to the

demagogue emotions

to degrade; to lower

demean

to lessen in value

depreciate

insane

deranged

derelict (three meanings) abandoned (adjective); negligent (adjective); a vagrant or bum (noun) to ridicule

deride

ridicule

derision dermatology

study of skin diseases belittling

derogator y

to discover

descr y desecrate

to damage a holy place

desiccate

to dry up; to wither to cease or stop

desist

lonely; deserted

desolate

contemptible; hateful

demeanor

behavior

despicable

demented

deranged; insane

despise

to scorn; to regard with disgust

despoil

to rob; to plunder

a person who is partly a god and partly

demigod human

despondent death; ending

demise

study of population trends

demography

to tear down

demolish

to discourage; to cause to lose spirit

demoralize demur demure

to object; to take exception to shy

a dictator

despot

poor; lacking

destitute desuetude

condition of disuse; extinction

desultor y rambling

wandering from subject to subject; a lessening of tension or hostility

détente

to ruin the reputation of; to blacken

denigrate

deter

to discourage; to hinder

occupant; inhabitant; resident

detergent

denomination the name or designation for a class of persons, such as a religious group

detonate

denizen

denouement denounce depict depilate

depressed; dejected

a cleansing agent explode

detoxify

remove the poison from

detract

to take away; to diminish

outcome; result to publicly condemn

to portray; to represent to remove hair from

deplete etc.)

to use up gradually (resources, strength,

deplore

to regret

detriment

harm; damage

devastate

to destroy; to overwhelm

deviate devious devoid

to turn aside; to digress sly; underhand completely without

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an enthusiastic follower

devotee

religious; pious; sincere

devout dexterity

skill; cleverness

diabolical

devilish; cruel crown

diadem

logical discussion

dialectic

transparent; very sheer and light

diaphanous

bitter criticism

diatribe

division into two parts

dichotomy dicker

to bargain; to argue over prices

diction

style of speaking

dictum

a positive statement

didactic much

instructive; inclined to lecture others too

diffident

shy; modest

diffuse

to spread; to scatter

digress

to wander off the subject broken down; falling apart

dilapidated

to expand; to become wider

dilate

slow or late in doing things

dilator y

a troubling situation

dilemma

a dabbler in the fine arts; one who is not

dilettante an expert

small

diminutive dint

disagreeing; harsh-sounding

discordant

discount (two meanings) reduction (noun); to disregard (verb)

power; force

dipsomaniac

drunkard

dire

dreadful; causing disaster

dirge

a funeral song or hymn

to disapprove of

discountenance

conversation; lecture

discourse

to disgrace; to cast doubt on

discredit

showing good judgment; cautious

discreet

inconsistency; difference

discrepancy

separate; not attached

discrete

good judgment

discretion

discrimination to distinguish

(two meanings) prejudice; ability

rambling; wandering

discursive

to scorn

disdain disgruntled

unhappy; discontented

dishearten

to discourage; to depress

disheveled

untidy to uncover; to dig up

disinter

impartial; not prejudiced

disinterested

gloomy; depressing

dismal

to take apart

dismantle

to cut or pull off limbs

dismember hard-working; industrious

diligent

without hope

disconsolate

to belittle; to put down

disparage

inequality; difference

disparity

dispassionate dispel

calm; impartial

to drive away

disperse

to scatter

disputatious

fond of arguing having a bad reputation

disarray

disorder; confusion

disreputable

disavow

to disown; to deny; to repudiate

dissection

cutting apart; analysis

dissemble

to conceal; to pretend

to pay out

disburse discern

to distinguish; to recognize; to perceive

disseminate

disciple

a follower

dissension

denial; renunciation

disclaimer disclose

to reveal; to make known

discomfiture disconcert

frustration; confusion to upset; to embarrass

dissertation dissident dissimulate dissipate

to scatter; to spread disagreement; opposition a written essay disagreeing to hide one’s feelings to waste; to scatter

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to break ties with; to part company

dissociate

immoral; unrestrained

dissolute

out of harmony

dissonant

to advise or urge against

dissuade

to expand; to swell; to stretch out

distend

to twist out of shape

distort

troubled

distraught

dither (preceded by in a) nervously excited or confused daily

diurnal

varying; different

divergent

several

divers

different

diverse

to deprive

divest

the act of foretelling the future

divination

to reveal; to make known

divulge

obedient; submissive

docile

shaky; senile

doddering doff

to throw off or away

feeblemindedness of old age

dotage

courageous; worthy

doughty

gloomy

dour douse

to put out (a fire); to extinguish

dowdy

shabby; untidy

senior or eldest member

doyen

Draconian

leftovers

drivel

childish nonsense; stupid talk amusing in an odd way

droll

drone (three meanings) a male bee (noun); an idle person (noun); to talk on and on monotonously (verb) waste matter

dross drudger y dual

dulcimer

sorrowful mournful; sad

dolorous dolt

a dull, stupid person home; residence

domicile donnybrook dormant dorsal

rough, rowdy fight asleep; inactive

pertaining to the back

dossier a complete group of documents containing detailed information

anger, resentment

dudgeon

having a definite opinion; authoritative

doleful

capable of being molded or shaped

ductile

dogmatic

to distribute; to give out sparingly

doubtful; questionable

dubious

dulcet

dole

hard, tiresome work

consisting of two people, items, or parts

stubbornly

low spirits

severe; cruel

dregs

doggedly

doldrums

trampled on; suppressed

downtrodden

dupe

pleasing to the ear a type of zither to trick; to deceive

duplicity

deceit; double-dealing; dishonesty

duress

force

dutiful

obedient

dwindle

to shrink; to become smaller

dynamo

a powerful person

dyspepsia

poor digestion

dysphasia

difficulty in speaking

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EARNEST–EXULT sincere; serious

earnest

realistic; coarse

earthy

to slowly decrease

ebb

elapse

to pass; to slip away overjoyed

enthusiastic

elated

eccentric

odd; out of the ordinary

electrify

pertaining to the church

rank of authority; level of power

echelon

brilliance; fame

éclat

a sad or mournful poem

elicit

to draw forth; to cause to be revealed

elite

the choice or best of a group of persons

selecting; choosing from various sources

elixir

eclipse

to overshadow; to outshine

ecology

study of the environment

ellipsis words

ecstatic

extremely happy

edifice

structure; building to improve someone morally; to instruct to draw or bring out

educe

weird; mysterious

eerie

to erase; to wipe out

efface

effective; adequate

effectual

unmanly; womanly; soft and weak

effeminate effer vescent

worn-out; barren

effete

power to produce an effect

efficacy

a likeness; an image

effigy

efflorescent

effronter y effulgent effusion emotion egalitarian men

shameful boldness shining forth brilliantly; radiant a pouring out; an uncontrolled display of pertaining to belief in the equality of all

egregious

remedy the omission in a sentence of a word or

eloquent

convincing or forceful in speech

elucidate

to make clear to avoid; to escape notice

elude elusive

difficult to grasp

elysian

blissful; heavenly abnormally thin

emaciated

to come forth; to send forth

emanate emancipate

to decorate

embellish

to steal

embezzle

to involve in trouble; to complicate

embroil

undeveloped; in an early stage

embr yonic emendation

selfishness; boasting about oneself remarkably bad; outrageous

famous; renowned

eminent emissar y

exit (noun and verb)

empathy empirical

emulous

one sent on a special mission

to send out; to give forth

emollient

emulate

correction

causing vomiting

emetic

emit

to set free (on) begin a journey or an endeavor

embark

emolument

a feeling of self-importance

egotism

egress

blossoming; flowering flowing out

effluent

ego

bubbly; spirited

to thrill

elegy

eclectic

edify

to throw out

eject

ebullient

ecclesiastical

an exclamation

ejaculation

something that soothes or softens profit; gain understanding another’s feelings based on experience rather than theory to imitate jealous; envious

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(of ) in love with

enamored

enclave a country, or part of a country, surrounded by another country encomium

an expression of high praise

encompass

to include; to surround

a repeat performance

encore

(upon) to trespass; to intrude

encroach

encumbrance

hindrance; obstruction filled with knowledge; comprehensive

encyclopedic

an expression of affection

endearment

environs

surroundings

envisage

to imagine; to form a mental picture messenger; agent

envoy

extremely long period of time

eon

temporary; short-lived

ephemeral

a long poem about heroic occurrences

epic epicure

one who seeks pleasure in fine foods

epigram

witty saying

epilogue

closing part of a speech or literary work

epiphany

appearance of a deity (god); revelation

endemic

confined to a particular country or area

epistle

energize

to rouse into activity

epitaph

inscription on a tomb

ener vate

to weaken

epithet

a descriptive word or phrase

to give the right to vote

enfranchise

to promote

engender

completely absorbed in

engrossed

to overwhelm

engulf

to increase in value or beauty; to improve

enhance

a puzzling situation; dilemma

enigma

a letter

epitome a typical example; a summary or condensed account particular period of history

epoch

equanimity

calmness; evenness of temperament

equestrian

a horseback rider

equilibrium

balance; stability

pertaining to horses

enigmatic

mysterious; puzzling

equine

enlighten

to inform; to reveal truths

equinox length

hostility; hatred

enmity

boredom

ennui

an outrageous and immoral act

enormity enrapture

to delight beyond measure

ensconce

to hide; to conceal; to settle comfortably to follow; to result from

ensue

to charm; to captivate

enthrall

the time when day and night are of equal

equipoise

balance

equitable

fair; just fairness; justice; impartiality

equity

doubtful; ambiguous

equivocal equivocate terms

to confuse by speaking in ambiguous to erase; to wipe out

eradicate

entice

to attract; to tempt

ergo

entity

independent being

erode

to wear away

erotic

pertaining to sexual love

study of insects

entomology

therefore

entourage

a group of personal attendants

err

entranced

filled with delight or wonder

errant wandering (in search of adventure); straying from what is right

entreaty

a request; a plea

entrenched entrepreneur enunciate

firmly established; dug in successful businessman; promoter to pronounce words clearly

to make a mistake

irregular; abnormal

erratic erroneous ersatz erstwhile

mistaken; wrong

artificial; inferior substitute formerly; in the past

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scholarly; learned

erudite

to increase; to grow rapidly; to intensify

escalate

a reckless adventure

escapade escarpment

steep cliff

to avoid; to keep away from

eschew

escrow (preceded by in) money deposited with a third person pending fulfillment of a condition for a select few; not generally known

esoteric

spying

espionage

to support (a cause)

espouse essay

(verb) to try; to attempt

estival

pertaining to summer separated; alienated

estranged

spiritual; airy

ethereal

pertaining to a particular race or culture

ethnic

the origin and development of words

etymology

science of improving the human race

eugenics

praise for a dead person

eulogy

euphemism substitution of a pleasant expression for an unpleasant one euphonious

having a pleasant sound; harmonious a feeling of well-being

euphoria

excruciating

exhilaration

urgent; critical

exigent

scanty; small in quantity

exiguous

a departure; a going out

exodus exonerate

to free from guilt or blame

exorbitant

excessive; unreasonable to drive out an evil spirit

exorcise

foreign; excitingly strange

exotic

to enlarge upon; to speak or write at

expatiate length

expatriate a person who is banished from, or leaves, his native country expectorate

to speed up; to make easy

expedite

to atone for explain in detail; make clear

explicit

clear; unambiguous; direct

exploit

to use for one’s own advantage to explain; to interpret

expound

to show clearly

expressly

evoke

to call forth; to produce

expunge

evolve

to develop gradually

expurgate

to aggravate; to make more violent

exact (two meanings) accurate (adjective); to demand or to require (verb) exalt

to raise in position; to praise

exasperate

to irritate; to annoy extremely

excise (two meanings) a tax on liquor, tobacco, etc. (noun); to cut out or off (verb) excoriate (two meanings) to scrape the skin off; to criticize sharply

replaceable

expendable

evince

exacerbate

to spit out practical; advantageous

expedient

explicate

to expel; to throw out

to bring out of the earth; to reveal

exhume

temporary; fleeting

evict

liveliness; high spirits

to warn

exhort

evanescent

to result; to happen finally

worthy of imitation

exemplar y

expiate

eventuate

to curse

execrate

mercy killing

not straightforward; tricky

to free from blame; to vindicate

exculpate

euthanasia

evasive

unbearably painful

extant

especially; particularly to erase to remove offensive passages; to cleanse still in existence

extemporaneous extenuating extinct extirpate extol extort

offhand; done without preparation

less serious

no longer in existence to destroy; to remove completely to praise to obtain by force

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to give up a prisoner to another authority

extradite

extrovert

an outgoing person full of enthusiasm

extraneous

unrelated; not essential

exuberant

extrapolate

to estimate; to infer

exude

extricate

to set free; to disentangle

exult

extrinsic

external; coming from outside

to discharge; to ooze to rejoice

FABRICATE–FUTILE

fabricate

(two meanings) to construct; to lie

faze

fabulous

incredible; imaginative

fealty

outward appearance

facade

aspect

facet

joking; sarcastic

facetious

easy; effortless

facile

to disturb; to discourage loyalty; devotion capable of being accomplished; suitable

feasible feat

deed or accomplishment

febrile

feverish

fecund

fertile; productive

facilitate

to make easy

feign

to pretend

facsimile

an exact copy; a duplicate

feint

a false show; a pretended blow

a minority within a larger group

faction

causing disagreement

factious

quick-tempered or quarrelsome

feisty

happiness

felicity

factitious

artificial

feline

factotum

an employee who can do all kinds of work

fell (two meanings) to knock down (verb); fierce or cruel (adjective)

power; ability; skill

faculty

misleading; deceptive

fallacious

capable of error

fallible fallow

inactive; unproductive

falter

to stumble; to hesitate a person with uncontrolled enthusiasm

fanatic fanciful

unreal; imaginative; unpredictable

fanfare

noisy or showy display

farcical

absurd; ridiculous hard to please

fastidious fatal

causing death

fatalistic inevitable

believing that all things in life are

fathom (two meanings) nautical measure of 6 feet in depth (noun); to comprehend (verb) fatuous fauna

foolish animals of a certain area

fawn (two meanings) a young deer (noun); to act slavishly submissive (verb)

pertaining to cats

a criminal

felon

felonious

treacherous; base; villainous a state of agitation or excitement

ferment

ferret (two meanings) a small animal of the weasel family (noun); to search or drive out (verb) eager; earnest

fer vent fer vid

very emotional

fester

to rot joyous; merry

festive fete fetid

to honor; to entertain foul-smelling

fetish object with magical power; object that receives respect or devotion fetter

to confine; to put into chains

fiasco

a total disaster

fiat

an official order

fickle fictitious

changeable in affections; unfaithful false; not genuine

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faithfulness

fidelity

something imagined

figment

fluster

to upset; to confuse

fluvial

pertaining to a river

filch

to steal

flux

filial

like a son or daughter

foible

the climax; end

finale finesse

diplomacy; tact

finicky

extremely particular; fussy limited; measurable

finite

one who stirs up a revolution

firebrand

pertaining to finances opening; groove; split

fissure

irregular; occurring in spurts

fitful

astonished; made speechless

flabbergasted flabby

flaccid

a weakness; minor fault

foil (two meanings) to prevent the success of a plan (verb); a person who, by contrast, makes another person seem better (noun) (on) to pass off merchandise which is inferior

foist

nonsense

folderol

a foolish action

folly

sky; heavens

firmament fiscal

state of continual change

flag (two meanings) a banner (noun); to droop or to slow down (verb) to whip

flaggelate

scandalous; shocking

flagrant

to stir up; to instigate

foment

foolish; reckless

foolhardy fop

an excessively vain man

foray

a sudden attack

forbearance

patience; restraint ancestor

forebear foreboding

a warning; an omen

foregone

long past

forensic

pertaining to a formal discussion or debate

flail

to strike freely and wildly

forerunner

ancestor; predecessor

flair

a knack; a natural talent

foreshadow

to hint

flamboyant flaunt

showy; conspicuous

to boast; to show off

flay (two meanings) to strip the skin off; to criticize sharply fledgling

a young, inexperienced person

fleece (two meanings) wool of a lamb (noun); to swindle (verb) flexible flinch flippant flora florid flotilla flotsam flout fluctuate

forestall to prevent by action in advance; to anticipate to give up

forfeit

to do without; to give up

forgo

formidable forte

dreadful; discouraging

strong point direct; frank

forthright

bendable to draw back; to cringe treating serious matters lightly plant life of a certain area flowery; ornate small fleet of ships floating cargo or wreckage to mock; to ridicule to move back and forth; to vary

fluent flowing; able to speak and/or write easily and clearly

fortitude

strength; courage

fortnight

two weeks; fourteen days

fortuitous

lucky; by chance

foster

to nourish; to encourage

fracas

a loud quarrel

fractious fracture frailty

irritable; quarrelsome; stubborn to break or to crack a weakness; a defect

franchise

special right or privilege

fraternal

brotherly

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dishonest; cheating

fraudulent

(with) filled

fraught

frantic; wild madness; fury

frenzy

a fresh water stream

freshet

extremely cold

frustrate

to prevent; to discourage

fugacious

pertaining to the passing of time

fulminate

to explode; to denounce disgusting; sickening; repulsive

rage; frenzy; fury

furtive

stealthy; secretive

fusion

a union; merging useless

futile

trivial; silly

frivolous

barren; yielding no results

furor

friction (two meanings) a rubbing together (noun); conflict or disagreement (noun) frigid

fruitless

fulsome

worried; irritated

fretful

fulfillment; realization

fruition

fray (two meanings) a noisy quarrel (noun); to unravel or to come apart (verb) frenetic

economical; thrifty

frugal

dirty; unkempt

frowzy

GADFLY–GYRATE

a person who annoys others

gadfly gaff

a hook to deny; to contradict

gainsay

thin and bony; bleak and barren

gaunt gazebo

an open structure with an enjoyable view

gazette

newspaper

gait

manner of walking

gelid

gala

festive

genealogy

galaxy a group of stars; any large and brilliant assemblage of persons gall

bitterness polite; noble

gallant

to stimulate; to startle into sudden activity

galvanize gambit

strategy; an opening one uses to advantage

gambol

to frolic; to romp about

gamut

the whole range or extent

gape

to stare with open mouth

garble

to distort

gargantuan garish

gigantic; huge

tastelessly gaudy

garland

a wreath of flowers

garner

to gather; to acquire

garnish

to decorate; to trim

garrulous gauche gaudy

talkative awkward; tactless flashy; showy

very cold; frozen family history to produce; to originate

generate generic

general; not specific; pertaining to a class

genesis

origin; beginning

genial

warm; friendly killing of a race of people

genocide genre genteel gentr y

an art form or class polite; refined upper class people

genuflect

to kneel; to bend the knee

germane

relevant; fitting

gerontology problems gesticulation ghastly ghoul gibberish

the study of older people and their lively or excited gesture

horrible; dreadful grave robber; ogre silly, unintelligible talk

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gallows from which criminals are hanged

gibbet

to scoff; to ridicule

give

dizzy; flighty; whirling

giddy

to cover with gold

gild

graphic

giving a clear and effective picture

grapple

to grip and hold; to struggle (two meanings)

grate

carefully; cautiously

gingerly

impressive; showy

grandiose

gratify

to please; to satisfy without payment; free

gird

to encircle

gratis

gist

main point; essence

gratuitous

glassy; smooth; shiny

glazed

to gather patiently and with great effort

glean

grievous

glib

fluent; smooth

grime

a malfunction; an error twilight; dusk

gloaming gloat

to look at or think about with great satisfaction to frown; to stare angrily at

glower glum

sad; gloomy

glutinous

causing grief or sorrow; distressing fierce; stern

grimace a distorted face; an expression of disapproval dirt

grime gripe

complaint

grisly

horrible; gruesome; ghastly

grit

stubborn courage extreme; vulgar

gross

gluey; sticky

sociable; friendly

gregarious

joy

glitch

free of cost; unnecessary

serious; somber

grave

glee

glissade a skillful glide over snow or ice in descending a mountain

to grind to shreds; to irritate

grotesque

absurd; distorted

glutton

one who eats or drinks too much

grotto

a cave

gnarled

knotty; twisted; roughened

grovel

to lower oneself to please another

a legendary dwarf-like creature

gnome goad

to encourage; to spur on

gorge (two meanings) a deep valley with steep sides (noun); to eat or to swallow greedily (verb) gor y

bloody

gossamer Gothic

medieval; mysterious

gouge (two meanings) overcharge

to dig out; to swindle or

a glutton; a person who eats excessively

gourmet

an expert of fine food and drink

gradient

a slope; a ramp

granar y

a storehouse for grain

grandiloquent style

exhausting

grueling gruff

rough or harsh in manner

guile

deceit; trickery sincere

guileless

light; flimsy; fine

gourmand

resentful; reluctant

grudging

pretentious; speaking in a pompous

a false appearance

guise gull

to trick; to deceive easily deceived; too trusting

gullible gumption

courage and initiative

gustator y

pertaining to the sense of taste

gusto

hearty enjoyment

gusty

windy; stormy

guttural gyrate

pertaining to the throat to rotate; to spin

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HABITAT–HYPOTHESIS

dwelling

habitat

trite; commonplace; overused

hackneyed

worn out from sleeplessness, grief, etc.

haggard

to bargain over a price

haggle

calm

halcyon hale

to make holy; to bless

hallucination

illusion; a false notion

to hinder; to keep someone from acting

hamper freely

unlucky

hapless

long speech

harangue

to annoy; to bother

harass

harbor (two meanings) a body of water providing ships with protection from winds, waves, etc. (noun); to conceal or hide (verb) courageous; sturdy

hardy

a clown

harlequin

harpy a greedy, grasping person; a scolding, nagging, bad-tempered woman upsetting; distressing

harrowing

to worry; to torment

harr y

a male deer snobbish; arrogant

haughty

haunt to appear as a spirit or ghost; to visit frequently; to disturb or distress haven

a safe place

havoc

great destruction

hazard

risk; danger recklessly; impulsively

headlong headstrong

hearth

careless; unmindful large and powerful; heavy

hefty

leadership or strong influence flight; escape hateful; abominable

heinous

blood defect

hemophilia

to announce; to usher in

herald

stubborn; willful rumor; gossip

fireplace

feeding on vegetation

herbivorous

tremendous in size, strength, or difficulty rejection of a religious belief

heresy

airtight; tightly sealed

hermetic

departing from acceptable beliefs

heterodox

heterogeneous

an omen or sign

harbinger

hearsay

heedless

herculean dependent upon mere chance

haphazard

hart

a pleasure-seeker

hegira

a symbol of high quality

hallow

hedonist

hegemony

healthy

hallmark

to bully

hector

different; unlike; dissimilar

period of success

heyday

pause or gap

hiatus hibernate winter

to be inactive, especially during the

hierarchy

a ranking, one above the other

hilarity

gaiety; joy

hircine

goat-like

hirsute

hairy; bearded theatrical; overly dramatic

histrionic hoard

to store away; to accumulate

hoar y

white with age or frost

hoax

a practical joke

hobgoblin a frightening apparition; something that causes fear hodgepodge

mixture

hogwash

meaningless or insincere talk

hoi polloi

common people; the masses

holocaust

complete destruction

homage

respect; honor

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a sermon

homily

homogeneous kind homophonic

composed of parts all of the same

hurtle

a crowd of people

horde

hybrid

the science of gardening

horticulture

shelter

hospice

black soil for fertilizing to dash; speed; run

husbandr y the science of raising crops; careful management

to shout in disapproval

hoot

lowliness; meekness

humus

to deceive

hoodwink

moist

humid humility

sounding alike

to sharpen

hone

monotonous; routine

humdrum

mixed; assorted

hymeneal

pertaining to marriage extreme exaggeration

hovel

a dirty, wretched living place

hyperbole

hover

to keep lingering about; to wait near at hand

hypercritical

excessive pride or self-confidence

hubris

a color; a shade

hue

humane

kind; compassionate

humbug

trick; hoax

fear of water; rabies

hydrophobia

overcritical; faultfinding

hypochondriac

a person with imaginary ailments

hypocrite one who pretends to be someone or something he is not an assumption; a theory

hypothesis

ICHTHYOLOGY–ITINERANT

study of fish

ichthyology

a statue or idol

icon

a rebel; one who breaks with tradition

iconoclast

one with very high standards

idealist

idiosyncrasy

a peculiar personality trait

excessive or blind adoration; worship of

idolatr y idols

charmingly simple or poetic

idyllic

a difficult or confusing situation

imbroglio imbue

to fill completely; to penetrate spotless; pure

immaculate

likely to happen; threatening

imminent

immolate to kill someone as a sacrificial victim, usually by fire immortal

not subject to death

immunity

freedom from disease

igneous

pertaining to fire

immutable

ignoble

dishonorable

impair

to weaken; to cause to become worse

impale body

to pierce with a sharp stake through the

ignominious ignoramus ilk

shameful; disgraceful a stupid person

type; sort; kind

illicit

unlawful; illegal

unchangeable

vague; not understandable

impalpable

without prejudice

impartial

illiterate

uneducated

impasse

a dead-end; a problem without a solution

illumine

to brighten; to inspire

impeach

to accuse

illusion illustrious imbibe

fake impression distinguished; bright to drink; to absorb

flawless; without fault

impeccable impecunious impede

without money; penniless

to hinder; to obstruct

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a barrier; an obstruction

impediment impel

push into motion; urge

inadvertent

unintentional

inalienable

not able to be transferred to another

impending

likely to happen soon

inane

imperative

extremely necessary

inanimate

imperious

domineering; haughty

inarticulate pertaining to speech that is not clear or understandable

not permitting passage

impermeable impertinent imperturbable

incandescent

very bright; shining

steady; calm

incapacitated

disabled; unable to function

acting without thought; impulsive

impetuous

in human form

incarnate

impinge

to strike; to collide; to encroach

incendiar y

impious

disrespectful toward God

incense

unbelievable

implausible

implement (two meanings) a tool (noun); to carry out or put into practice (verb) implication an indirect indication; a statement that suggests something suggested, but not plainly expressed

implicit imply

to suggest

import (two meanings) significance; meaning (noun); to bring in from a foreign country (verb) importune

to persistently ask; to beg

impostor a person who goes about under an assumed name or character impotent

powerless; lacking strength

blood-red; flesh-colored

incarnadine

a stimulus; a moving force

unbending; inflexible; merciless

to imprison

incarcerate

impetus

implacable

lifeless; dull; dead

rude; disrespectful

not capable of being affected; hardened

impervious

silly; meaningless

causing fire; stirring up trouble to inflame; to enrage

incentive

something that incites to action

inception

beginning; start

incessant

continuous; without pause

inchoate

at an early stage; just beginning

incipient

beginning to exist or appear sharp; keen

incisive incite

to urge to action; to stir up

inclement (usually refers to weather) harsh; unfavorable; severe disguised

incognito

rambling; not logically connected

incoherent

unsuited; inappropriate

incongruous inconsequential

unimportant certain; undeniable

imprecation

a curse

incontrovertible

impregnable

unconquerable

incorrigible

bad beyond correction or reform

incredulous

skeptical; disbelieving

impromptu

without preparation; offhand

impropriety pertaining to something that is not proper or suitable improvident

wasteful

improvise

to do without preparation

impudent

disrespectful; shameless

impugn to attack a person with words; to challenge a person in regard to motives

increment

an increase; a gain

incriminate to charge with a crime; to connect or relate to a wrongdoing incubus

nightmare

inculcate (in or upon) to teach earnestly; to influence someone to accept an idea

freedom from punishment

incumbent (two meanings) resting or lying down (adjective); one who holds a political office (noun)

impute to accuse a person of some wrongdoing; to attribute a fault or a crime to a person

incur to bring upon oneself; to run into some undesirable consequence

impunity

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a raid; an invasion

incursion

incapable of being tired out

indefatigable

incapable of being erased

indelible indemnify

to insure; to repay

indicative

signifying; implying

indict to charge with a crime; to accuse of a wrong-doing native to a particular area; inborn

indigenous

extremely poor

indigent

angry as a result of unjust treatment

indignant

inborn

inherent

restraint; reserve

inhibition

inimitable

indoctrinate

to teach someone principles or beliefs

iniquity

harmful; unfriendly not able to be imitated or equaled wickedness to begin

initiate

lazy

indomitable

unconquerable; unyielding

injunction

indubitable

unquestionable; certain

inkling

to cause; to bring about gentle treatment; tolerance drunk not able to be described; unspeakable

ineluctable

(oneself ) to work one’s way into another’s

ingratiate favor

permanent

ineffable

ungrateful person

ingrate

indissoluble

inebriated

simple; innocent; naive

ingenuous

inimical

indulgence

clever

ingenious

unquestionable; without doubt

induce

(on or upon) to break a law; to violate; to

infringe trespass

indisputable

indolent

the breaking of a law or rule

infraction

inevitable; inescapable

innate

a command; an order a hint inborn; existing from birth harmless

innocuous innovate

to introduce a new idea

innuendo

indirect remark; hint

inordinate

unusual; excessive unable to be satisfied

inept

unfit; bungling; inefficient

insatiable

inert

without power to move; inactive

inscrutable

unavoidable; sure to happen

inevitable

unyielding

inexorable

certain; without mistakes

infallible infamous detestable infantile

having an extremely bad reputation;

infectious passing on a disease with germs; likely to spread; contagious infer infernal infidel

to conclude; to derive by reasoning hellish; fiendish; diabolical unbeliever

infinitesimal exceedingly small; minute (pronounced my-newt) infirmity inflated influx

weakness; feebleness puffed up; swollen a flowing in

treacherous

insidious

insightful having a penetrating understanding of things; mentally alert and sharp to hint; to suggest

insinuate insipid

childish; immature

mysterious; difficult to understand

tasteless; dull boldly disrespectful

insolent insolvent

bankrupt; unable to pay creditors

insomnia

sleeplessness carefree; happy-go-lucky

insouciant

to provoke; to stir up

instigate

insubordinate insular

disobedient

pertaining to an island; detached; isolated

insuperable insurgence insurrection

unconquerable rebellion; action against authority uprising; rebellion

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entire; left whole; sound

intact

essential; whole

integral

insightful; knowing by a hidden sense

intuitive

to fill to overflowing; to flood

inundate

integrate

unify; to bring together into a whole

inured

integrity

honesty; sincerity

invalidate void

deprive of legal value; to make null and

invariably

constantly; uniformly; without changing

intellectual high degree

intelligent; having mental capacity to a highly educated, cultured people

intelligentsia inter

to bury to prohibit; to ban

interdict interim

meantime; period of time between one who takes part in a conversion

interlocutor

an intruder

interloper

a period of time between two events

interlude interminable

endless starting and stopping; periodic

intermittent

to insert between; to estimate

interpolate

to place between

interpose

interregnum pause; interval; any period during which a nation is without a permanent ruler interrogate

to question

interstellar

between or among stars to come between

inter vene

intimate (two meanings) private or personal (adjective); to imply (verb) intimidate

make afraid; threaten

intolerant

bigoted; narrow-minded hard to manage

intractable

stubborn; refusing to give in

intransigent intrepid

fearless; courageous

intricate

complex; hard to understand

intrinsic essential; pertaining to a necessary part of something introspective

looking into oneself

introvert a person who is concerned with his own thoughts or feelings

(to) accustomed to

strong verbal abuse

invective inveigh

(against) to make bitter verbal attack

inveigle

trick; lure; deceive to turn inside out or upside down

invert inveterate

firmly established; deep-rooted

invidious

causing resentment; offensive

invigorate

to fill with energy

invincible

not able to be defeated; unconquerable to call upon

invoke

not able to be hurt; immune to attack

invulnerable iota

a small quantity easily angered

irascible ire

anger; wrath

iridescent displaying a wide range of colors like those of the rainbow annoying; bothersome

irksome ironic

contrary to what was expected senseless; unreasonable

irrational

irreconcilable

unable to agree

irredeemable

hopeless; unable to be brought back

irremediable

unable to be corrected or cured beyond repair

irreparable irrepressible

unable to be controlled or restrained

irresolute

indecisive; doubtful; undecided

irreverent

disrespectful

irrevocable itinerant

final; unchangeable traveling from place to place

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JADED–KNUCKLE

ired; worn out; dulled

jaded

jargon vocabulary peculiar to a particular trade or group of people; meaningless talk; gibberish jaundiced (two meanings) pertaining to a yellowed skin; prejudiced jaunt

short trip; excursion

jaunty

carefree; confident

jilt

extreme patriotism

jinx jocose

joking; humorous

jocular

humorous

jostle

to bump; to push

jovial

jolly; good-natured

to place side by side constantly changing

range of knowledge to set on fire; to excite

kindle

relative; family, tribe, or race

kinetic

pertaining to motion

kismet

destiny; fate a compulsion to steal

kleptomania

to bring bad luck to

science of law

to stick out; to project

kindred

to reject; to cast off

jingoism

a small group ruling a country

ken

to throw goods overboard

jettison

junta

kaleidoscopic

goods cast overboard to lighten a ship

jetsam

a pleasure trip; an excursion

juxtapose

to joke; to make light of

jest

junket

jut

danger

jeopardy

a point of time; a crisis

juncture

jurisprudence

to sneer; to mock

jeer

pertaining to the throat or neck

jugular

a tricky, deceitful person

knave

knead to work dough, clay, etc. into a uniform mixture knell the sound made by a bell rung slowly for a death or funeral

jubilation

celebration; rejoicing

knoll

judicious

wise; showing sound judgment

knuckle (under) to yield; (down) to apply oneself vigorously

a terrible destructive force

juggernaut

a small rounded hill

LABYRINTHINE–LUXURIANT

complicated; intricate

labyrinthine

to tear ( flesh) roughly; to mangle

lacerate lachr ymose

lackadaisical

uninterested; listless

slavish follower

lackey lackluster vapid laconic

tearful

lacking brilliance or liveliness; dull or

laity

lambent softly bright or radiant; running or moving lightly over a surface

laminated lampoon languid

using few words; concise

languish

pertaining to milk

lank

laden

burdened; loaded

lapidar y

a slow person; one who falls behind

to mourn

lament

lactic

laggard

religious worshipers who are not clergy

larceny

covered with thin sheets, often plastic a sharp, often harmful satire sluggish; drooping from weakness to become weak or feeble

long and slender a dealer in precious stones theft

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gifts that have been given generously

largess

lustful or lewd; inciting sexual desire

lascivious

a feeling of weakness and weariness

lassitude

present, but hidden

latent

to the side; sideways

lateral

freedom; margin

latitude laudable

praiseworthy

laureate

worthy of praise or honor to wash or bathe

lave

very generous; extravagant

lavish lax

careless or negligent room for freedom of action; margin

leeway

legerdemain

sleight of hand; deception

lenient

mild; lax; permissive

leonine

lion-like; fierce; authoritative

facial features

lineaments

pertaining to language

linguistic

to treat as a celebrity

lionize

liquidate (two meanings) to get rid of by killing; to wind up the affairs of a business moving gracefully; agile or active

lissome

feeling no interest in anything; indifferent

listless

exact; precise; word for word

literal lithe

graceful; flexible lawsuit

litigation

livid darkened or discolored; pale from anger or embarrassment reluctant; unwilling

loath

to hate; to feel disgust for

loathe

place

locus

lesion

an injury; a wound

lode a rich source of supply such as a mineral deposit

lethal

deadly; fatal

lofty

lethargic

dull; slow-moving; sluggish

leviathan

anything vast or huge; a sea monster lightness of body or spirit; lack of seriousness

levity levy

to impose and collect taxes pertaining to lust or sexual desire

lewd

dictionary

lexicon

liaison a bond; a connection; an illicit relationship between a man and a woman a drink; a beverage

libation

a false statement in written form

libel

giving freely; not strict

liberal

one who leads an immoral life

libertine

the words of an opera

libretto licentious liege lieu

lawless; immoral; lewd

lord; master (in lieu of ) in place of; instead of

lilliputian

tiny; narrow-minded

very high; formal; proud

logistics military operations dealing with the supply and maintenance of equipment to linger; to hang around

loiter loll

to lean or lounge about; to droop a long life

longevity lope

to move along with a swinging walk

loquacious lot lout

fate an awkward, stupid person humble; ordinary

lowly

giving off light; shining

lucent

clear; easy to understand; rational or sane

lucid

profitable; producing wealth or riches

lucrative

ridiculous

ludicrous lugubrious lull

easily bent; flexible

lunacy

limpid

clear, transparent

lunar

lineage

ancestry; descent

lupine

sad; mournful

to soothe or calm

luminous

limber

talkative

bright insanity; madness pertaining to the moon wolflike; fierce

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lurch

to move suddenly forward

lush

lurid

shocking; glowing; sensational

lustrous

lurk

to lie concealed in waiting; to stay hidden

abundant; rich shining; bright rich; extravagant

luxuriant

MACABRE–MYTHICAL

horrible; gruesome

macabre

deceitful; tricky

Machiavellian

to cut, slash, or crush so as to disfigure

mangle

shabby; filthy

mangy

machination

evil design

manifest

evident; obvious

macroscopic

visible to the naked eye

manifold

many; varied

whirlpool

maelstrom magnanimous

generous

important person in any field

magnate

size; extent

magnitude

maim to cripple; to deprive of the use of some part of the body clumsy; unskillful; awkward

maladroit malady

disease; illness

malaise

discomfort; uneasiness

malapropism

word humorously misused

malcontent

one who is dissatisfied

malediction

curse wrong-doer; villain

malefactor

malevolent showing ill will or hatred; very dangerous, harmful malfeasance

spiteful; vengeful

malicious malign

to speak badly of

malignant malingerer work malleable malodorous mammoth manacle mandarin mandate mandator y

wrongdoing

evil; deadly one who pretends to be sick to avoid

manipulate (two meanings) to handle or manage with skill; to influence a person in a bad way

bad-smelling; stinking huge; enormous handcuff; restraint influential person an order; a command required; obligatory

to raid; to plunder

maraud

pertaining to marriage

marital

pertaining to the sea

maritime

marquee a rooflike shelter, such as glass, projecting above an outer door warlike

martial

a strict disciplinarian

martinet martyr

one who suffers for a cause

mar vel

to be amazed; to wonder one who enjoys his own pain and

masochist suffering

huge; bulky

massive masticate

to chew

maternal

motherly

a social organization in which the matriarchy mother is the head of the family matrix

a place of origin excessively sentimental

maudlin maul

capable of being changed; adaptable

to set free

manumit

to injure; to handle roughly

mausoleum

large tomb for many bodies

maverick

a rebel; a nonconformist

mawkish

sickeningly sweet; overly sentimental

maxim

a proverb or saying

meager

inadequate; of poor quality

mean (three meanings) nasty or offensive (adjective); inferior or low (adjective); an average (noun)

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to wander aimlessly

meander

interfering; curious

meddlesome

to settle a dispute; to act as a go-between

mediate

ordinary; average; neither good nor bad

mediocre

to think deeply; to ponder

meditate

medley a mixture; a musical selection combining parts from various sources megalomania false impression of one’s own greatness; tendency to exaggerate sad; depressed

melancholy

noisy fight

melee

smoothly flowing; sweet-sounding

mellifluous

overly emotional

melodramatic

remembrance; a souvenir

memento menace

a threat; a danger

ménage

household; domestic establishment collection of wide or strange animals

menagerie

lying; false

mendacious

a beggar

mendicant menial

low; degrading

mentor

adviser

a miniature world

microcosm mien

manner; bearing wandering; moving from place to place

migrator y

environment; setting

milieu

ready and willing to fight

militant

a thousand years

millennium mimic

to imitate

minion

a devoted follower; a highly regarded person very small

minuscule

minute (two meanings) sixtieth part of an hour (pronounced min-ut); very small and insignificant (pronounced my-newt) insignificant details; trivia

minutiae

an apparition or illusion

mirage

mire (two meanings) wet, swampy ground (noun); to involve in difficulties (verb) mirth

joy; amusement; laughter hater of mankind

misanthrope

misapprehension

miscegenation mixture of races, especially through marriage unlucky accident; bad luck

mischance mercantile

pertaining to merchants; commercial

mercenar y

motivated only by a desire for money changeable; fickle; erratic

mercurial

gaudy; showy; attractive in a cheap,

meretricious flashy way mesa walls

a flat-topped elevation of land with steep rock to hypnotize

mesmerize

metamorphosis

comparison (without like or as)

metaphor metaphysics mete

a change; a transformation

pertaining to beyond what is natural

(out) to distribute in portions momentarily dazzling; swift

meteoric meteorology

study of weather and climate

doubt; suspicion

misgiving misnomer

an error in listing the name of a person

misogamy

hatred of marriage

misogynist

woman-hater

missive

letter

mitigate

to make less severe; to become milder

mnemonic

pertaining to memory

mobile

movable; flexible

mock

metropolis

large city

modish

pollution; poisonous environment

a criminal offense less serious than

misdemeanor a felony

modicum

miasma

a vicious person; a villain

miscreant

excessively careful; finicky

courage; spirit

misinterpret; misjudge

misconstrue

meticulous

mettle

a misunderstanding

modulate mogul

to ridicule; to insult; to lower in esteem a small amount fashionable; stylish to soften; to tone down powerful person

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molest

to disturb; to bother

motif

mollify

to pacify; to calm; to appease

motley

to shed, such as feathers and skin

mottled

molt

melted

molten

monastic

pertaining to a monk; self-denying

monetar y

pertaining to money

murky

monologue

long speech by one person

muse

monotheism

belief in one god

muster

monumental

great; important

musty

doubtful; debatable

mute

delay; postponement

moratorium

customs; traditions; morals dying

moribund

gloomy; ill-humored

morose

generous

mortal

destined to die; causing death

mortify

to embarrass; to humiliate

dark; unclear; gloomy to think deeply to gather together stale; moldy silent to disfigure; to cripple rebellious

mutinous

sarcastic; biting

mores

worldly

mutilate

depressing; gruesome

mordant

varied; having many parts

munificent unyielding; unified

morbid

(over) to study or think about

mundane

monolithic

moot

to confuse; to mix up

multifarious

a paper, book, etc. written about a sin-

monograph gle subject

a phony; a fraud; a charlatan

mulct to punish with a fine; to obtain money by extortion mull

one who watches or warns

monitor

spotted; blotched; streaked

muddle

government by one ruler

monarchy

diverse; assorted; having different colors

mountebank

very important

momentous

theme; central idea

muzzle

to restrain; to gag

myopic

near-sighted; having a limited point of view

myriad

infinitely vast in number an unquestioning follower

myrmidon

imaginary; fictitious

mythical

NABOB–NUTRIMENT

nabob

a very wealthy or powerful person

nadir

lowest point

naive

simple; unsophisticated

narcissistic

conceited; vain

nascent

coming into being; being born

natation

the act or art of swimming

nativity

birth

naught

nothing

nautical nebulous

pertaining to ships, sailors, navigation hazy; vague; uncertain

necromancy witch nefarious negate negligent nemesis achieve

magic, especially that practiced by a wicked

to deny; to make ineffective careless something that a person cannot conquer or

neologism

new use of a word

neophyte

a beginner; a novice

nepotism

favoritism shown toward relatives

nether

lower; under

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to irritate; to annoy

nettle

to make ineffective; to counteract

neutralize

noncommittal

nexus group

connection, tie, or link among the units of a

nicety

delicacy; subtlety

niche

recess or hollow in a wall

to spend excessive time on unimportant

niggle details

quick and light in motion

nimble

place of great peace or happiness

nir vana

pertaining to night

nocturnal

nonpareil

unequaled; unrivaled to confuse; to perplex

nostalgia

homesickness; longing for the past

nostrum

quack medicine; supposed cure-all having a bad reputation; infamous

notorious

a beginner

noxious

harmful

nuance etc.

delicate variation in meaning, tone, color,

nub

a small, rounded mass or lump

nodule

person or thing of little importance

novice

total rejection of established laws

nihilism

having no definite point of view

nonentity

nonplus

stingy; miserly

niggardly

unconcerned; casual

nonchalant

a lump or small piece

noisome

foul-smelling; harmful or injurious

nubile suitable for marriage, in regard to age and physical development

nomadic

wandering; homeless

nugator y

a set of names or terms

nomenclature

nullify

in name only; not in fact

nominal

nuptial

coin collector

pertaining to marriage to feed; to sustain

nurture

a period of immaturity

nonage

to make useless or ineffective

numismatist

something that does not logically

non sequitur follow

worthless; invalid

food; nourishment

nutriment

OAF–OVOID

oaf

a dunce or blockhead

oasis

a place which offers a pleasant relief stubborn; hard-hearted

obdurate

obeisance a bow or similar gesture expressing deep respect obese

very fat

obfuscate oblation purposes obligator y oblique

to confuse; to bewilder; to perplex an offering for religious or charitable

objectionable; offensive

obnoxious

obscurant a person who tries to prevent the spread of knowledge dim; not clear; not easily understood

obscure

excessively submissive; overly attentive

obsequious

a funeral rite or ceremony

obsequy obsess person

to control the thoughts or feelings of a going out of use; becoming extinct

obsolescent required; mandatory slanted; indirect

obliterate

to erase; to do away with

oblivious

forgetful; unmindful

obloquy strong disapproval; bad reputation resulting from public criticism

stubborn

obstinate obstreperous obtrude

boisterous; unruly

to push something toward or upon a person

obtuse

slow to comprehend

obviate

to prevent

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western; opposite of oriental

occidental

to close; to shut; to block out

occlude

opt

( for) to choose one who sees the good side of things

optimist

occult

hidden; secret; mysterious

optimum

ocular

pertaining to sight

opulent

odious

disgusting; hateful

oracular

giving off a displeasing or strong smell

odoriferous

a long journey

odyssey

garbage; waste parts

offal

meddling; interfering

officious ogle

to look at with desire

ogre

monster; hideous being pertaining to smell

olfactor y

oligarchy government in which power is in the hands of only a few individuals majestic

Olympian

an event which indicates the future

omen

threatening; indicating evil or harm

ominous omnifarious

of all kinds

omnipotent

all-powerful

omniscient

all-knowing eating any kind of food; absorbing

omnivorous everything

a furious attack

onslaught onus

a burden; a responsibility not transparent; not letting light pass

opaque through opiate

narcotic; causing sleep or relief one who takes advantage of a situation

opportunist oppress

rich; luxurious mysterious; predicting a speech delivered on a special occasion

oration

orbit a curved path, such as a planet takes around the sun to order; to establish; to arrange

ordain

ordeal difficult or painful experience; a primitive form of trial

to rule harshly; tyrannize

opprobrious

shameful; disgraceful

law; regulation

ordinance

fundamental; essential

organic

Orient (two meanings) an area of the Far East, such as Asia (noun); to adjust or adapt to (verb) orifice

mouth; opening

ornate

showy; highly decorated

ornithology

study of birds accepting the usual or traditional beliefs

orthodox orthography

correct spelling

oscillate to swing or move back and forth, like a pendulum to change into bone; to become rigid

ossify burdensome; heavy

onerous

the best; most favorable

apparent; conspicuous

ostensible ostentatious ostracize oust

showing off; boastful to banish; to exclude

to drive out; to expel

outwit

to trick; to get the better of

overt

open; aboveboard; not hidden

ovine

of or like a sheep

ovoid

egg-shaped

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PACIFY–PYRRHIC

to calm down

pacify pact

an agreement song of praise or joy

paean

pleasant to the taste

palatable

magnificent

palatial

study of prehistoric life

paleontology

pall (two meanings) something that covers or conceals (noun); to become wearisome or unpleasant (verb) to ease; to lessen

palliate

pale; dull

pallid

parity

equality; similarity

parley

discussion; conference

parody a work which imitates another in a ridiculous manner

parrot

to repeat or imitate without understanding

parr y

to avoid something such as a thrust or blow

parsimonious partisan

palpitate

to beat rapidly; to tremble

passé

muscle paralysis trivial; worthless

panacea

a cure-all; an answer for all problems

panache

self-confidence; a showy manner general; widespread

pandemic

pandemonium

pang

wild disorder; confusion

an expression of praise

panegyric

a sharp pain suit of armor; any protective covering

panoply

unlimited view; comprehensive survey

panorama

a simple story giving a moral or religious

parable lesson

a model; an example

paradigm

paradox a statement that seems contradictory, but probably true a model of excellence or perfection

paragon parameter

boundary; limits

paramount

chief; supreme

paranoia mental disorder characterized by a feeling of being persecuted paraphernalia paraphrase parched pariah

a sudden outburst; a fit

paroxysm

obvious; capable of being touched or felt

paltr y

local; narrow; limited

parochial

palpable

palsy

dangerous

parlous

personal belongings; equipment to reword; to restate

dried up; extremely thirsty an outcast

stingy; miserly

a strong supporter of a cause old fashioned; out-of-date

passive pastoral

submissive; unresisting pertaining to the country; rural

patent (two meanings) a government protection for an inventor (noun); evident or obvious (adjective) paternal pathogenic pathos

fatherly causing disease pity; deep feeling

patriarch an early biblical person regarded as one of the fathers of the human race patrician patrimony

aristocratic inherited right; heritage

patronage the control of power to make appointments to government jobs patronize down to paucity peccadillo

(two meanings) to be a customer; to talk scarcity; lack a minor offense

pectoral

pertaining to the chest

peculate

to steal; to embezzle

pecuniar y

pertaining to money

pedagogue

a schoolteacher

pedantic

tending to show off one’s learning

pedestrian (two meanings) one who walks (noun); ordinary or dull (adjective)

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a record of ancestors; a line of descent

pedigree

peer (two meanings) closely (verb)

an equal (noun); to look

without equal; unmatched

peerless

hard to please; irritable

peevish

having a negative effect; insulting

pejorative

transparent; clear

pellucid

pelt (two meanings) skin of a fur-bearing animal (noun); to throw things at (verb) pertaining to punishment

penal

a strong liking for; an inclination

penchant

pert

bold; saucy

to unsettle; to disturb

perturb

to read carefully

peruse

to spread throughout; to pass through

per vade

contrary; cranky

per verse

expressing sorrow for sin or wrongdoing

pessimist

pensive

dreamily thoughtful

petrify

penur y

extreme poverty

petrology

observable; recognizable

perceptible

damnation; ruin; hell

perdition

relevant; to the point

pertinent

penitent

to observe

clearness, as of a statement

perspicuity

per vert

perceive

keenness of judgment

perspicacity

anything that hangs or is suspended

common worker

to lead astray; to corrupt one who sees the worst in everything to turn to rock; to paralyze with fear study of rocks

unimportant; minor

petty petulant

irritable; rude

phalanx

closely massed body of persons

phenomenon

to travel from place to place

philander

peremptor y

decisive; final; not open to debate

philanthropy

lasting for a long time; perpetual deceitful; treacherous; unfaithful

perfidious

of necessity

perforce perfunctor y perigee

done without care; routine

point nearest to the earth dangerous; risky

perilous

peripher y outside boundary; unimportant aspects of a subject periphrastic perjur y

said in a roundabout way

making a false statement while under oath

extraordinary person, thing, or event to engage in various love affairs

peregrinate

perennial

giving human qualities to a non-

personification human being

pendant

peon

to endure; to continue

persevere

a desire to help mankind; generosity

philately

stamp collecting

philippic

a bitter verbal attack

philistine

uncultured; common

phlegmatic

unemotional; cool; not easily excited intense fear

phobia

a bird which symbolizes immortality

phoenix picaresque

pertaining to an adventurous wanderer trifling; petty

piddling piecemeal

bit by bit; gradually

pied

many-colored; variegated

piety

reverence; devotion

permeate

to spread throughout

pernicious

deadly; destructive

pigment

peroration

the concluding part of a speech

pilgrimage

perpetrate

to do something evil; to be guilty of

pillage

to rob by violence

perpetuate

to cause to continue

pillor y

to expose to public ridicule or abuse

perplexity

confusion

pinnacle

perquisite

something additional to regular pay

pious

dye; coloring matter a journey to a holy place

peak; highest point religious

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stimulating to the taste; exciting interest

piquant

to irritate or annoy

pique

of or like a fish

piscine

concise; to the point

pithy

small share or amount

pittance

speaking or writing several languages

polymorphic

brilliant show or display

pomp

central; crucial

placard

small poster

ponderous

placate

to soothe; to calm

porcine

plagiarism

to think deeply; to consider carefully

ponder

calm

placid

heavy; burdensome of or like a pig capable of being carried

portable

door; gate; entrance

portal

warning; foreshadowing

portentous

claiming another’s work to be one’s own

plague (two meanings) a contagious disease (noun); to torment; to trouble (verb)

stout; large

portly

future generations

posterity

plaintive

sorrowful; sad

posthumous

platitude

a dull or trite remark

postulate granted

spiritual; free from sensual desire

platonic

plaudit applause; (in the plural) any expression of approval

having many forms belief in many gods

polytheism

pivotal

placebo harmless, phony medicine; something said or done to soothe

many-colored

polychromatic polyglot

unexpected difficulty; a trap

pitfall

a coward

poltroon

occurring after death to assume without proof; to take for

drinkable

potable

powerful; strong

potent

plausible

apparently true, fair, or reasonable

potentate

ruler; monarch

plebeian classes

pertaining to a member of the lower

potential thing

capacity for being or becoming some-

full; complete; absolute

plenar y

abundance

plethora

a drink

potion potpourri

a mixture practical

pliant

easily bent; adaptable

pragmatic

plight

a sad or dangerous situation

prate

ploy

precarious

a gimmick; a trick

pluck (two meanings) (noun)

to rob; to take by force

plunder plutocracy poach podium poignant

to pull at (verb); courage

to test; to measure

plumb

to talk extensively and pointlessly; to babble

rule by the wealthy class

to trespass a platform keenly distressing; affecting the emotions

to be, come, or go before

precede precedent the future

an act that may be used as an example in a rule of conduct

precept

cliff

precipice precipitate precipitous précis

uncertain; dangerous; risky

to bring about an action suddenly extremely steep

brief summary

polarize

to separate into opposing groups

preclude

polemic

a controversy or argument

precocious

prematurely developed

precursor

a forerunner; predecessor

politic

diplomatic; shrewd

to prevent; to shut out

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predator y

living by plunder, exploitation, etc.

predicate

to declare; to assert a liking; preference; inclination

predilection predispose

to make susceptible

preeminent

standing out above all others

to dress oneself carefully or smartly

preen

adapted for seizing or grasping

prehensile something

to investigate; to examine

probe

honesty; integrity

probity

inclination; tendency

proclivity

to plan beforehand

premeditate

to beget or produce

procreate

prod

to urge; to poke or jab wasteful

first in importance or time

prodigal

premise drawn

statement from which a conclusion is

prodigious

forewarning; hunch

premonition preponderance dominance

superiority in quantity or power; absurd; ridiculous

preposterous

privilege or right

prerogative

to indicate or warn in advance knowledge of things before they

prescience happen

anticipation, especially of something

presentiment evil

influence; importance

prestige

presumptuous pretentious

showing disrespect for sacred things

profess

to acknowledge; to admit frankly

proffer

to offer

profligate

shamelessly immoral; extremely wasteful

profound

very deep

profuse

abundant

progeny

descendants

prognosticate

showy; putting on airs

proliferate

prolix

prevail

to succeed; to gain the advantage

prologue

first; chief

primar y

of the earliest times or ages

primeval

primogeniture primordial primp prismatic pristine privation

state of being the first born first; original

to dress up in a fussy way many-colored uncorrupted; in its original state loss or lack of something essential

one who belongs to the working class to expand; to increase productive; fertile

prolific

a false reason or motive; an excuse

formal; proper

to predict; to foretell

projectile a bullet, shell, grenade, etc., for firing from a gun proletarian

to lie

skill; competency

proficiency

pretext

prevaricate

enormous; vast

profane

boldly assuming

abnormal; beyond what is natural

preternatural

prim

designed to get conformity at any cost

to obtain; to secure

procure

premier

presage

to postpone; to delay

procrastinate

procrustean an introduction

prelude

privy (to) having knowledge of something private or secret

tediously long and wordy introduction

promenade walking promiscuous

a stroll or a walk; an area used for sexually loose

promontor y

piece of land that juts out

promulgate

to announce; to advocate

prone

reclining; lying flat; inclined

propagate

to spread; to multiply

propensity

inclination; tendency

prophetic propinquity propitious

predicting nearness; closeness favorable

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proponent doctrine

a person who supports a cause or

dull; commonplace; unimaginative

prosaic

to denounce; exile

proscribe

proselyte a person who has changed from one religion to another; a convert prospectus project

a report describing a forthcoming

protagonist

main character

protean

changeable; variable

protégé another

one who has been guided or instructed by the etiquette observed by diplomats

protocol

the original; first of its kind; a model

prototype protract

to draw out; to prolong

protrude

to stick out; to project

proverbial

well-known

provident

having foresight

provincial

countrified; narrow; limited

provisional proviso

temporary a condition; a stipulation

provoke

to anger; to irritate; to annoy

prowess

skill; strength; daring

proximity

nearness in place or time

proxy

one who acts in place of another

prude

an overly proper person

prudence

caution; good judgment

prune to cut off or lop off such as twigs, branches, or roots prurient

psyche

the human soul or spirit

puerile

childish; immature

pugilist

a boxer eager to fight; quarrelsome

pugnacious

powerful; strong

puissant

beauty

pulchritude lying flat; thrown or fallen to the ground

prostrate

a fake or assumed name

pseudonym conformity; appropriateness

propriety

false; counterfeit

pseudo

lustful; obscene; lewd

pertaining to the lungs

pulmonar y

crush or grind into powder; totally

pulverize destroy

to beat or thrash with the fists

pummel

pun the use of words alike in sound but different in meaning very exact; precise

punctilious pundit

a learned man; an expert or authority

pungent having a sharp taste or smell; severely critical or sarcastic pertaining to punishment

punitive puny purge

weak; inferior to cleanse; to purify strict; rigid; harsh

puritanical purloin

to steal

purport

to claim to be

pur vey

to furnish; to supply

pusillanimous

supposed; believed

putative putrefy pyre pyretic

cowardly; fearful

to rot; to decay a funeral fire in which the corpse is burned pertaining to fever

pyromaniac Pyrrhic victor y

one who likes to start fires; arsonist success gained at too high a cost

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QUACK–QUOTIDIAN an untrained doctor; a pretender to any skill

quack

a four-footed animal

quadruped

essential quality

quiddity

to lose courage; to shrink with fear

quail

petty objection or argument

quibble

a swamp; a difficult situation

quagmire

a line of people waiting their turn

queue

to gulp; to drink in large quantities

quaff

a search

quest

quidnunc

a gossip or busybody at rest; motionless

quaint way

strange or unusual in a pleasing or amusing

quiescent

qualm

a feeling of uneasiness

quietus activity

a puzzling situation; a dilemma

quandar y

an animal that is being hunted down

quarr y

to cancel; to set aside (as an indictment)

quash

to tremble; to shake

quaver

extremely idealistic; romantic; not practical odd; questioning; puzzled

quizzical

to subdue; to calm down

quell

to tremble; to shake

quixotic

uneasy; nauseated

queasy

the pure and concentrated essence

a witty or sarcastic remark

quip

quiver

a wharf

quay

quintessence of something

quirk a peculiar characteristic of a person; a sudden twist or turn

resembling; seeming

quasi

finishing stroke; anything that ends an

daily

quotidian

complaining

querulous

a question

quer y

RABBLE–RUTHLESS mob; disorderly crowd

rabble

intense; furious or raging; mad

rabid

to torment; to torture

rack

storyteller

raconteur

extreme; complete; violent

radical rail

(at or against) to complain bitterly

railler y

good-humored ridicule

raiment

clothing; garments

rakish

carefree; lively

rambunctious ramification

a result; a consequence; a branch widespread; raging

rampant ramshackle rancid

restless; hard to control

shaky; ready to fall apart

having a bad taste or smell; stale; repulsive

rancor

bitter resentment; hatred

rankle

to cause irritation; to fester

rant

to speak in a loud or violent manner taking by force; greedy

rapacious

a close relationship; harmony

rapport

rapt completely absorbed in; overcome with joy, love, etc. rarefy

to make less dense; to refine

rash (two meanings) a skin irritation (noun); reckless or daring (adjective) raspy

harsh; grating

ratify

to officially approve of

ratiocinate ration rational

to reason

a fixed portion; a share sensible; reasonable

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to make an excuse for

rationalize

irritating or harsh in sound

raucous

to damage; ruin

ravage

raze

reek

to destroy; to level to the ground

shining; glowing

refurbish

to make new; to freshen up

kingdom; region

refute

rebuff

to refuse; to snub

regal

to scold; to blame contradiction; opposing argument

rebuttal

disobedient; hard to manage

recalcitrant

to withdraw or disavow a statement or opinion

recant

to summarize; repeat briefly

recapitulate

to go or move back; to withdraw

recede

recess (two meanings) thing; a pause or rest

stubborn; hard to manage

refulgent

realm

rebuke

to give off; emit

refractor y

extremely hungry; greedy

ravenous

repetitious; unnecessary

redundant

a cut or notch in some-

to prove wrong, such as an opinion pertaining to a king; splendid to entertain

regale

regenerate to re-create; to reform morally; to replace a lost part of the body one who governs

regent

the killing of a king

regicide

a system of government

regime

a regular system (of exercise, diet, etc.)

regimen regressive

moving in a backward direction to rush or surge back, as undigested food

recidivist

a person who goes back to crime

regurgitate

recipient

one who receives

rehabilitate

interchangeable; mutual

reciprocal

to give in return

reciprocate

hermit; one who shuts himself off from the

recluse world recoil reconcile

to bring into agreement or harmony

recondite

difficult to understand; profound to survey; to check out in advance

reconnoiter

to tell or relate, as a story

recount

coward; traitor

recreant

recrimination rectify

to pay back

reimburse

to repeat

reiterate

to make young again

rejuvenate

to banish; to assign to an inferior position

relegate to retreat; to draw back

countercharge

to correct; to make right honesty; moral uprightness

rectitude

to restore to useful life

unyielding

relentless

significant; pertaining to the subject

relevant

to give up; to let go

relinquish

to enjoy; to take delight in

relish

intended to correct

remedial

to remember

reminisce

negligent

remiss

recumbent

lying down; reclining

remission offenses

recuperate

to get well

remonstrate

recur

to happen again deliverance from sin; a rescue

redemption

having a pleasant odor

redolent redoubtable redress

formidable; commanding respect

to set right; to remedy

capable of being corrected

remediable

a lessening; a forgiveness as of sins or to protest; to complain regret for wrongdoing

remorse

remuneration renaissance

payment for a service rebirth; renewal; revival

renal

pertaining to the kidneys

rend

to split; to tear apart

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a meeting; appointment

rendezvous

a deserter; a traitor

renegade

to go back on one’s word

renege

a delay; rest

respite

shining brightly; dazzling

resplendent

repayment; a giving back

restitution

renounce

to give up (a belief )

restive

restless; uneasy; impatient

renovate

to make new; to repair

restrain

to hold back; to control

résumé

a summary

resurge

to rise again

reparation compensation; something done to make up for a wrong or injury done a quick; witty reply

repartee repast

a meal

repellent something that drives away or wards off (insects, etc.) reaction; aftereffect

repercussion

special skills or talents one possesses;

repertoire collection repine

to complain; to fret to fill up again

replenish replete

well-filled

repose

to rest; to sleep

reprehensible shameful

deserving criticism or blame;

to scold

reprimand

retaliation; revenge

reprisal reproach

to blame; to scold

reprobate

a wicked person a rebuke

reproof repudiate

to reject; to disown

repugnant

distasteful; disgusting

repulse

to drive back; to repel

reputed

supposed to be

requiem

funeral hymn; mass for the dead

requisite

required or necessary; indispensable

requite

to make a return or repayment

rescind

to cancel; to repeal

residue

that which remains

resilient

recovering quickly; elastic

resolute

very determined

resonance resourceful

resuscitate to revive from apparent death or from unconsciousness revenge; repayment for an evil act

retaliation

having a good memory; remembering

retentive reticent

silent or reserved in manner

retinue

body of attendants or followers a short, witty reply

retort

to take back (a statement); to withdraw

retract

to cut down or reduce expenses

retrench

deserved punishment

retribution

to get or bring back

retrieve

to control; to subdue

repress

fullness of sound able to deal effectively with problems

revival; rebirth

resurrection

retroactive applying to a period before a certain law was passed retrogressive

going backward; becoming worse

retrospect events

(preceded by in) looking back on past

revelation

something made known; a disclosure noisy merrymaking

revelr y

reverberate

to echo; to resound

to honor; to respect

revere

a daydream

reverie

to abuse; to slander

revile rhetorical

concerned with mere style or effect vulgar; indecent

ribald rife

frequently occurring; widespread

rift

a break or split

righteous rigorous

behaving justly or morally strict

risible

laughable; funny

risqué

daring or indecent; not proper

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rite

a religious ceremony; a solemn act strong; hearty

robust

a dishonest person; a scoundrel

rogue

rote (preceded with by) from memor y, without thought for meaning round; fat

rotund

overwhelming defeat

rout

to break apart; to burst

ruse

a skillful trick or deception

rustic

pertaining to the country

rustle sound

(two meanings) to steal; to make a swishing cruel; merciless

ruthless

elementary; basic

rudimentar y rue

to consider carefully; to mediate on

rupture

a list

roster

ruffle (two meanings) a wrinkle or a ripple (noun); to irritate or to annoy (verb) ruminate

jolly; carefree

rollicking

hoodlum; lawless person

ruffian

to regret; to be sorrowful

SACCHARINE–SYNTHETIC overly sweet

saccharine

the violation of anything sacred

sacrilege

extremely holy

sacrosanct

deriving pleasure from inflicting pain on

sadistic others saga

satiated

satisfied; filled up

satirical

sarcastic; ironic

saturate

to soak; to fill up gloomy; sluggish

saturnine a long story of adventure wise

sagacious sage

pertaining to clothes or tailoring

sartorial

obscene; lusty significant; conspicuous

salient saline

salty

sallow

sickly pale healthful

salubrious salutar y salutator y salvage

healthful; wholesome a welcoming address, as at a graduation to rescue; to save from destruction hypocritical in regard to religious

sanctimonious belief sanction sangfroid sanguinar y sanguine sapient sardonic

a person of extensive learning

savant

a wise person

salacious

to stroll; to walk leisurely

saunter

to authorize; to give permission calmness; composure bloody cheerful; optimistic wise mocking; scornful

savoir faire any situation

tact; knowledge of just what to do in

savor

to enjoy, as by taste or smell

scant

inadequate in size or amount one who takes the blame for others

scapegoat

extremely severe or harsh, such as a

scathing remark

a split or break

schism

a tiny amount; a speck

scintilla

to sparkle; to twinkle

scintillate scion

an offspring; a descendant

scoff

to ridicule

scope

range; extent

scourge a whip or a lash; a person or thing that punishes or destroys scrupulous

honest; ethical; precise

scrutinize

to examine closely

scurrilous

coarsely abusive; vulgar

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scurr y

run about; to hurry

sham

scuttle

to sink (a ship); to abandon

shambles

sear

to burn; to scorch fatty

sebaceous

shard

a pretense a slaughterhouse; great disorder a fragment embarrassed; bashful

sheepish

seclude

to keep apart; to isolate

shibboleth

secrete

to hide or conceal

shiftless

secular

worldly; nonreligious

shoal

quiet; calm; serious

sedate

a slogan; a password lazy; inefficient

a shallow place in the water; a reef

shortcomings

defects; deficiencies

sedentar y

sitting most of the time

shrew

sediment residue

material that settles on the bottom;

shroud a cloth or sheet in which a corpse is wrapped for burial

rebellion

sedition

hard-working; industrious; diligent

sedulous

run-down; shabby

seedy

to boil; to be violently agitated

seethe seismic

semblance

hissing

sibling

a brother or sister

simian

pertaining to an ape or monkey

simile

a comparison using like or as

pertaining to earthquakes

simony

the sin of buying or selling church benefits

outward appearance

simper

to smile in a silly way

pertaining to mental weakness due to old age

senile

sibilant

a nagging, bad-tempered woman

an image; a likeness

simulacrum

sensate

pertaining to feeling

simulate

sensual

pertaining to enjoyment of food and sex

simultaneous

pertaining to enjoyment of art, music, etc.

sensuous sententious remarks

concise; including proverbs and brief

sentient

conscious; capable of feeling

sentinel

a guard

sepulcher

tomb; burial vault

sequel an event or literary work that follows a previous one sequester

to separate; to set aside angelic; pure

seraphic

serendipity a talent for making desirable discoveries by accident calm; peaceful

serene serpentine serrated ser vile ser vitude sever shackle

winding having tooth-like edges like a slave slavery; bondage

to cut in two; to separate to keep prisoner; to restrain

to pretend; to imitate

job with no responsibility

sinecure sinewy singular

occurring at the same time

tough; firm; strong extraordinary; remarkable; exceptional

sinister

threatening evil; ominous

sinuous

curving; winding

siren skeptic

an attractive but dangerous woman one who doubts stingy person; miser

skinflint skittish

restless; excitable; nervous

skuldugger y skulk slacken

trickery; deception

to sneak around; to lie in hiding become loose; to relax

slake to lessen (thirst, desire, anger, etc.) by satisfying; to quench slander

to make a false statement against someone

slattern

an untidy woman

sleazy sleek

cheap; flimsy smooth and shiny

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to slide or glide

slither

lazy

slothful

untidy; dirty; careless

slovenly

causing sleep

soporific

(off ) to discard; to shed

slough

immature; pretentious

sophomoric

dirty; filthy

sordid sot

a drunkard

smirk

to smile in an affected or offensive way

sobriquet

nickname; assumed name

smite

to strike forcefully

sovereign

a monarch or other supreme ruler

smolder to burn without flame; to keep feelings concealed smug

self-satisfied

snare

to trap

sneer

to look at with contempt; to scorn; to deride

roomy; convenient

spacious

warlike; brave; disciplined

Spartan

a sudden burst of energy

spasm

not genuine; pleasing to the eye but

specious deceptive

snicker

to laugh in a half-suppressed way

specter

snippet

a small fragment

speculate (two meanings) to meditate; to participate in a risky business transaction

snivel

to whine; to complain

sober

not drunk; serious nickname; assumed name

sobriquet sodden

soaked; damp

sojourn

a brief stay or visit

solar

pertaining to the sun

solecism ungrammatical usage; an error or inconsistency solicit to ask; to seek; to try to get an order in business concern; anxiety

solicitude

act of talking to oneself

soliloquy

solipsistic pertaining to the theory that only oneself exists or can be proved to exist loneliness

solitude solon

a wise man

solvent (two meanings) having the ability to pay a debt (adjective); a substance that dissolves another (noun) somber

dark; gloomy

somnambulate somniferous somnolent

person who is difficult to understand

sphinx splenetic

bad-tempered; irritable

sporadic

infrequent; irregular

spr y

full of life; active foam

spume

comfort

solace

a ghost; a phantom

walk in one’s sleep causing sleep

drowsy; sleepy

sonorous

producing a deep, rich sound

sophistr y

a deceptive, tricky argument

deceitful; counterfeit

spurious

to reject

spurn

filthy; dirty

squalid staccato

made up of short, abrupt sounds

stagnant

not flowing; stale; sluggish

staid

sedate; settled a deadlock; a draw

stalemate stalwart

strong; sturdy

stamina

endurance; resistance to fatigue attitude; posture

stance stark

complete; harsh; severe

static

inactive; motionless standing still; not moving

stationar y statute

law; rule firm in purpose; dependable; constant

steadfast stench

a foul smell

stentorian stereotyped sterling

very loud not original; commonplace of high quality; excellent

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stigma

mark of disgrace

substantiate

stilted

artificially formal

subterfuge

stint

to be sparing; to conserve salary

stipend

to specify; to arrange definitely

stipulate stoic pain

showing no emotion; indifferent to pleasure or

stolid

impassive; having little emotion

strait water

a position of difficulty; a narrow passage of a plan, scheme, or trick

stratagem

to spread about; to scatter

strew

striped; marked with lines

striated stricture

negative criticism; a restriction

strident

harsh sounding; loud and shrill strict; tight

stringent strut

to walk in a proud manner; to show off

stultify

make absurd or ridiculous; render worthless

stupefy

to stun; to amaze

stygian

dark; gloomy

stymie

to hinder; to block

suave

polished; sophisticated secretly; confidentially

sub rosa subaqueous

underwater

subjective

not objective; personal

subjugate

to conquer

sublimate

to make a person act noble or moral majestic; elevated or lofty in thought

sublime subliminal

subconscious; unaware

submissive

yielding; humbly obedient

subordinate suborn

to hire for an unlawful act following; occurring later

subsequent subser vient capacity subside subsidiar y assist

of lower rank

submissive; helpful, in an inferior

trickery; deceit

auxiliary; supplementary; serving to

underground

subterranean

tending to overthrow or undermine

subversive

concise; brief and to the point

succinct

assistance; help; relief

succor succulent

juicy

succumb

to yield; to give in the right to vote

suffrage

gloomy; showing irritation

sullen sully

to soil, stain, or tarnish hot and moist

sultr y

luxurious; lavish; extravagant

sumptuous

various; assorted

sundr y

retired because of old age

superannuated

proud; haughty

supercilious

on the surface; shallow

superficial

excessive; unnecessary

superfluous

heavenly

supernal

extra; more than necessary

supernumerar y supersede

to take the place of

super vene

to take place or occur unexpectedly lying on the back

supine

to replace

supplant

flexible

supple suppliant

begging; asking humbly

supplicate

to pray humbly; to beg an excessive amount

surfeit surly

rude; bad-tempered to guess

surmise

to go beyond; to overcome

surmount surreptitious

acting in a sneaky way substitute

surrogate sur veillance

to become quiet; to settle down

to prove; to confirm; to support

supervision; close watch

sustenance

nourishment

susurration

whispering; murmuring

suture

to join together, as with stitches

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slender; graceful

svelte

symbiosis mutual dependence between two different organisms

dark-complexioned

swarthy

to wrap closely or fully

swathe

one who is fond of luxuries and pleasure

sybarite

a flatterer; a parasite

sycophant

wooded; pertaining to the forest

sylvan

symmetrical

balanced; well-proportioned

synchronize

to happen at the same time

synthesis

a combination; a fusion

synthetic

not genuine; artificial

TABLEAU–TYRO dramatic scene or picture

tableau

forbidden; unacceptable

taboo

a systematic listing by columns or rows

tabulation

silent; not expressed

tacit

speaking very little

taciturn tactics

plan; method; strategy

tactile

pertaining to sense of touch to infect; to harm a person’s reputation

taint

a good luck charm

talisman

to count; to make a record of

tally tangent

touching

tangible

real; capable of being touched

tantalize

to tease or torment

tantamount

equivalent to

a small lake or pool

tarn

to soil; to discolor; to stain

tarnish

temporize action

to be indecisive; to be evasive; to delay an

tenacious

holding on; persistent; stubborn

a doctrine; a belief

tenet

capable of being stretched; elastic

tensile tentative

for the time being; experimental

tenuous

slender; flimsy; without substance the holding or possessing of anything

tenure

lukewarm

tepid

terminate

to put an end to; to conclude

terminus

a boundary; a limit

earthly; living on land

terrestrial terse

brief; to the point

testy

irritable

thanatology

to linger; to delay

theocracy

taunt

to ridicule; to tease

therapeutic of disease

like a bull

taut

tight; tense cheap; showy; flashy

tawdr y tawny

yellowish-brown

tedious

boring; monotonous

teeming

overfilled; pouring out

temerity

reckless boldness; rashness

temper temperate temporal

(verb) to moderate; to soften or tone down not extreme; moderate pertaining to time

pertaining to dancing

terpsichorean

tarr y

taurine

biased; favoring a cause

tendentious

government by religious leaders

thesaurus dictionary

thrall threnody

pertaining to the treatment and curing pertaining to heat

thermal

thespian

the study of death and dying

a book of synonyms and antonyms; a an actor

a slave a funeral song

throes a violent struggle; pains (of childbirth); agony (of death) throng

a crowd

thwart

to prevent or hinder

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fearful; cowardly

timorous

a faint color; a trace

tinge

tirade a long angry speech; an outburst of bitter denunciation huge

titanic

to tickle; to excite agreeably

titillate

to laugh in a self-conscious or nervous way

titter

token (two meanings) sign or symbol (noun); slight or unimportant (adjective) large, heavy book

tome

tasty

toothsome

very hard work; intense pain

travail

an absurd or inadequate imitation

travesty

dangerous; deceptive; disloyal

treacherous

a book or writing about some particular

treatise subject

three times as much

treble

trembling; quivering

tremulous

keen or incisive; vigorous; effective

trenchant

fear; alarm

trepidation

to invade; to enter wrongfully

trespass

trouble

tribulation

topple

to overturn; to fall over

tributar y

torpid

inactive; sluggish

tribute a gift; an acknowledgment to show admiration

twisting; bending

torsion

the human body excluding the head and limbs

torso

twisting; winding

tortuous

causing extreme pain

torturous

standard; a test or criterion for quality

touchstone

poisonous; harmful

toxic

easy to manage

tractable

to speak badly of; to slander

traduce trait

a characteristic; a quality calm; peaceful

tranquil

to go beyond; to overcome

transcend

transcendental supernatural; going beyond ordinary experience or belief trangression

violation of a rule or law temporary; passing

transient

lasting a short time; brief

transitor y

letting light pass through

translucent transmute transform transparent

to change from one form to another; to

savage; brutal; cruel

truculent

a self-evident, obvious truth

truism

to shorten; to cut off

truncate

a club

truncheon tr yst

a secret meeting swollen; bulging

tumid tumult

great noise and confusion

turbid

muddy; unclear wild disorder; violent motion

turbulence

swollen

turgid

confusion

turmoil

baseness; shameful behavior

turpitude

tutelage

to be revealed or become known; to occur

twain

trappings

articles of dress; equipment

tycoon

a shock; an aftereffect

(to) to submit; to yield

truckle

transpire

trauma

worn out; stale; commonplace

trivia matters or things that are very unimportant; trivialities

tussle easily seen through; clear

group of three

trinity trite

a stream flowing into a river

tyro

a struggle; a fight instruction two a wealthy businessman a beginner

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UBIQUITOUS–UXURIOUS present everywhere

ubiquitous

infected

ulcerous

a final demand or proposal

ultimatum umbrage

a feeling of resentment

unanimity

agreement; oneness

unconscionable

inconspicuous; not noticeable

not manageable; disorderly unpleasant to taste or smell unharmed; uninjured

unreasonable; excessive

unseemly

not in good taste

untenable

unable to be defended or upheld

unwieldy

hard to manage because of size or weight

unwitting

unintentional; unaware

oily; excessively polite

unctuous undue

unobtrusive

unscathed

crude; clumsy

uncouth

absolute; not lessened

unsavor y

weird; strange

uncanny

unmitigated

unruly

unable to be attacked

unassailable

unaware

unmindful

lying beyond; hidden

ulterior

untidy; sloppy

unkempt

inappropriate; unreasonable to move or sway in wavelike motion

undulate

uproarious

clear; definite

unequivocal

accurate; not going astray or missing the

unerring mark

to scold; to find fault with

upbraid

loud; outrageously funny

urbane

refined; suave; citified

urchin

a mischievous child

unfledged

not feathered; immature

ursine

like a bear

unilateral

one-sided

usurp

to seize illegally

unimpeachable uninhibited

above suspicion; unquestionable free; not restricted

usur y excessive amount of money charged as interest

unique

being the only one of its kind

utilitarian

unison

harmony; agreement

utopian

broad; general; effective everywhere or in

universal all cases

useful; practical perfect; ideal overly fond of one’s wife

uxorious

VACILLATE–VULPINE vacillate to sway back and forth; to hesitate in making a decision a wanderer

vagabond vagar y

an odd notion; an unpredictable action

vagrant

valid

true; logical; sound to approve; to confirm

validate valor

courage; bravery

a homeless person; a wanderer

vain conceited; excessively proud about one’s appearance vainglorious valedictor y

courageous; brave

valiant

boastfully proud saying farewell

vanguard vanity vanquish vapid

the front part excessive pride; conceit to defeat uninteresting; tasteless; tedious

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having different colors; diversified

variegated

to brag or boast

vaunt

to change direction

veer

lead a dull, inactive life

vegetate

forceful; furious

vehement

corrupt; able to be bribed

venal

bitter quarrel or feud

vendetta

an outward show that misrepresents

veneer

worthy of respect

venerable

to regard with respect

venerate

excusable; minor

venial

poisonous; spiteful; malicious

venomous

to give release to; to be relieved of a feeling

vent

daring; adventurous; risky

venturesome

truthful; honest

veracious verbatim

word for word

verbiage

overabundance of words

verbose

wordy

verdant

green; flourishing

verisimilitude

true; actual; genuine

veritable verity

truth

vernacular

vertex

whirling; dizzy; unstable

vex viable viaduct viands

vigilant

watchful

vignette

a short literary sketch; a decorative design

vilify

to speak evil of; to defame

vindicate

to clear of guilt or blame

vindictive

spiteful; seeking revenge representative of the best (especially of

vintage wines)

viper a poisonous snake; a malignant or spiteful person a loud, bad-tempered woman; a shrew

virago virile

masculine; manly

virtuoso

an expert; a skilled person

virulent

deadly; poisonous; harmful the face; appearance

visceral pertaining to instinctive rather than intellectual motivation sticky

viscous

a distant view to weaken; to impair

vitiate vitreous

of or like glass

vitriolic

biting; sharp; bitter to scold; to criticize

vivify

to give life to; to enliven

vixen

female fox; ill-tempered woman

energy; enthusiasm

vestige a trace; visible evidence of something that is no longer present veteran

to compete

vituperate top; highest point

vertiginous ver ve

native language; informal speech

good at many things; ser ving many

versatile purposes

food

victuals

vista

pertaining to spring

vernal

to make a victim of; to swindle or cheat

victimize

visage the appearance of truth

unpredictable changes; ups and downs

vicissitudes

vie

speed

velocity

viceroy a representative; a deputy appointed by a sovereign to rule a province

an experienced person to irritate; to annoy capable of living; workable; practicable a bridge various foods

vicarious taking the place of another person or thing; substituted

loud; shouting

vociferous vogue

fashion; style

volant

capable of flying

volatile

unstable; explosive

volition

free will

voluble

talkative; fluent

voluminous

large; copious

voluptuous

sensual; shapely

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extremely hungry; greedy

voracious

loyal follower

votar y

defenseless; open to attack

vulnerable

to grant; to allow or permit

vouchsafe

showing poor taste or manners

vulgar

like a fox; clever

vulpine

WAIF–ZEST

waif

a homeless person to give up (a right)

waive

to indulge oneself; to roll around in

wallow

pale; weak; tired

wan

to gradually decrease in size or intensity

wane

wangle to manipulate; to obtain by scheming or by underhand methods wanton

reckless; immoral

warble

to sing melodiously

warp

to bend out of shape; to pervert

war y

cautious; watchful a spendthrift; one who wastes

wastrel

to sway; to be uncertain

waver wax

to grow in size or intensity of utmost importance

weighty

to direct one’s way

wend

to coax or to persuade

wheedle

to stimulate; to make sharp

whet

whimsical

unpredictable; changeable

wield to handle (a tool); to exercise control (over others) contrary; stubborn

willful wily

tricky; sly

wince windfall winsome

to shrink, as in pain, fear, etc.; to flinch unexpected good fortune pleasing; charming

in spite of all; nevertheless

withal

withered; shriveled

wizened

sorrow; grief

woe

ferocious

wolfish

(to) accustomed (adjective)

wont

everyday; ordinary

workaday

a ghost; an apparition

wraith

to quarrel

wrangle

anger; rage

wrath

to twist; to pull

wrench wrest

to take away by force

wroth

angry produced or shaped

wrought

wr y produced by distorting the face (a wry grin); ironic (wry humor) xenophobia xyloid yen

fear of foreigners or strangers

pertaining to wood an intense desire; a longing

yoke

to join together; to link

zany

comical; clownishly crazy

zeal

great enthusiasm

zealot

a fanatic

zenith

the highest point

zephyr

a gentle, mild breeze

zest

hearty enjoyment

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100 Tests to Strengthen Your Vocabulary

This vocabulary section consists of 100 Vocabulary Tests. Each test consists of 10 multiple-choice questions, including SAT-type words. Practically all the words whose meanings you are tested on in these 100 tests are among the 3,400 words in the SAT Word List beginning on page 363. These 100 Vocabulary Tests provide you with an opportunity to make sure that you really know the meanings of the hundreds of words you are being tested on. Several of these words are likely to appear on your actual SAT exam. We suggest that you use the following procedure while you are taking these 100 tests: 1. Take Vocabulary Test 1. 2. Turn to the Answer Keys beginning on page 458. 3. For each word that you got wrong, jot down the word on a “Special List” of your own. 4. Make up a sentence using each word that you got wrong on Vocabulary Test 1. 5. Repeat the above procedure for Vocabulary Tests 2, 3, 4—right on through Vocabulary Test 100. 6. When you have finished taking the 100 Vocabulary Tests, go back to your “Special List.” See whether you really know the meanings of these words by having someone else test you on them. For those words you still have trouble with, look up their meanings in a dictionary. Compose three sentences including each of these “troublemakers.” Gentle reminder: Knowing the meanings of many of the words in these 100 tests is likely to raise your score in the Verbal (Critical Reading) sections, Sentence Completions, and Reading Comprehension.

Directions for the 100 Vocabulary Tests Each vocabulary question consists of a word in capital letters, followed by five lettered words or phrases. Choose the word or phrase that is most nearly the same in meaning as the word in capital letters. Since some of the questions require you to distinguish fine shades of meaning, consider all choices before deciding which is best.

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Vocabulary Test 1 1.

2.

FILCH (A) hide (B) swindle (C) drop (D) steal (E) covet URBANE (A) crowded (B) polished (C) rural (D) friendly (E) prominent

9.

REDUNDANT (A) necessary (B) plentiful (C) sufficient (D) diminishing (E) superfluous

7.

APLOMB (A) caution (B) timidity (C) self-assurance (D) shortsightedness (E) self-restraint

10.

ATROPHY (A) lose leaves (B) soften (C) waste away (D) grow (E) spread

8.

THERAPEUTIC (A) curative (B) restful (C) warm (D) stimulating (E) professional

Vocabulary Test 2

9.

TRANSMUTE (A) remove (B) change (C) duplicate (D) carry (E) explain

RESILIENCE (A) submission (B) elasticity (C) vigor (D) determination (E) recovery

DECANT (A) bisect (B) speak wildly (C) bequeath (D) pour off (E) abuse verbally

1.

ANTITHESIS (A) contrast (B) conclusion (C) resemblance (D) examination (E) dislike

2.

5.

HERETICAL (A) heathenish (B) impractical (C) quaint (D) rash (E) unorthodox

3.

FACETIOUS (A) obscene (B) shrewd (C) impolite (D) complimentary (E) witty

1.

TRUNCATE (A) divide equally (B) end swiftly (C) cut off (D) act cruelly (E) cancel

6.

COALESCE (A) associate (B) combine (C) contact (D) conspire (E) cover

4.

DIATRIBE (A) debate (B) monologue (C) oration (D) tirade (E) conversation

2.

OSCILLATE (A) confuse (B) kiss (C) turn (D) vibrate (E) whirl

7.

CHARLATAN (A) clown (B) philanthropist (C) jester (D) dressmaker (E) quack

5.

MALEDICTION (A) curse (B) mispronunciation (C) grammatical error (D) tactless remark (E) epitaph

3.

INOCULATE (A) make harmless (B) infect (C) cure (D) overcome (E) darken

8.

GAUCHE (A) clumsy (B) stupid (C) feebleminded (D) impudent (E) foreign

6.

AGGREGATE (A) result (B) difference (C) quotient (D) product (E) sum

4.

PERUSAL (A) approval (B) estimate (C) reading (D) translation (E) computation

3.

4.

ANALOGY (A) similarity (B) transposition (C) variety (D) distinction (E) appropriateness

10.

ATTRITION (A) annihilation (B) encirclement (C) counterattack (D) appeasement (E) wearing down

Vocabulary Test 3

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VOCABULARY BUILDING THAT IS GUARANTEED TO RAISE YOUR SAT SCORE • 417 5.

6.

7.

8.

9.

10.

QUERULOUS (A) peculiar (B) fretful (C) inquisitive (D) shivering (E) annoying AUTONOMY (A) tyranny (B) independence (C) plebiscite (D) minority (E) dictatorship MACHINATIONS (A) inventions (B) ideas (C) mysteries (D) plots (E) alliances SCHISM (A) government (B) religion (C) division (D) combination (E) coalition PUSILLANIMOUS (A) cowardly (B) extraordinary (C) ailing (D) evil-intentioned (E) excitable TERMINOLOGY (A) technicality (B) finality (C) formality (D) explanation (E) nomenclature

3.

4.

5.

6.

7.

FIASCO (A) disappointment (B) turning point (C) loss (D) celebration (E) complete failure VAGARY (A) caprice (B) confusion (C) extravagance (D) loss of memory (E) shiftlessness GRAPHIC (A) serious (B) concise (C) short (D) detailed (E) vivid CONNOTATION (A) implication (B) footnote (C) derivation (D) comment (E) definition TORTUOUS (A) crooked (B) difficult (C) painful (D) impassable (E) slow

8.

FULMINATING (A) throbbing (B) pointed (C) wavelike (D) thundering (E) bubbling CIRCUMVENT (A) freshen (B) change (C) control (D) harass (E) frustrate


PROLIFIC (A) meager (B) obedient (C) fertile (D) hardy (E) scanty

2.

ASSUAGE (A) create (B) ease (C) enlarge (D) prohibit (E) rub out

3.

DECORUM (A) wit (B) charm (C) adornment (D) seemliness (E) charity

4. PHLEGMATIC

(A) (B) (C) (D) (E) 5.

INTREPID (A) quick-witted (B) brutal (C) fearless (D) torrid (E) hearty

6.

ACTUATE (A) frighten (B) direct (C) isolate (D) dismay (E) impel

7.

MOUNTEBANK (A) trickster (B) courier (C) scholar (D) cashier (E) pawnbroker

8.

LACONIC (A) terse (B) informal (C) convincing (D) interesting (E) tedious


STIPEND (A) increment (B) bonus (C) commission (D) gift (E) salary

9.

2.

LITIGATION (A) publication (B) argument (C) endeavor (D) lawsuit (E) ceremony

10.

CARTEL (A) rationing plan (B) world government (C) industrial pool (D) skilled craft (E) instrument of credit

tolerant careless sensitive stolid sick

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418 • VOCABULARY BUILDING THAT IS GUARANTEED TO RAISE YOUR SAT SCORE 9.

10.

BOORISH (A) sporting (B) tiresome (C) argumentative (D) monotonous (E) rude

7.

PUGNACIOUS (A) bold (B) combative (C) brawny (D) pug-nosed (E) valiant

5.

AMELIORATE (A) favor (B) improve (C) interfere (D) learn (E) straddle

ERUDITE (A) modest (B) egotistical (C) learned (D) needless (E) experienced

8.

ASTRINGENT (A) bossy (B) musty (C) flexible (D) corrosive (E) contracting

6.

CHARY (A) burned (B) careful (C) comfortable (D) fascinating (E) gay

9.

ESCARPMENT (A) threat (B) limbo (C) cliff (D) behemoth (E) blight

7.

CORPULENT (A) dead (B) fat (C) full (D) organized (E) similar

AMENITIES (A) prayers (B) ceremonies (C) pageantries (D) pleasantries (E) social functions

8.

ENIGMA (A) ambition (B) foreigner (C) instrument (D) officer (E) riddle

Vocabulary Test 7

9.

INEPT (A) awkward (B) intelligent (C) ticklish (D) tawdry (E) uninteresting

10.

INVETERATE (A) evil (B) habitual (C) inconsiderate (D) reformed (E) unintentional


2.

ACRIMONIOUS (A) repulsive (B) enchanting (C) stinging (D) snobbish (E) disgusting EMBRYONIC (A) hereditary (B) arrested (C) developed (D) functioning (E) rudimentary

10.

INEXORABLE (A) unfavorable (B) permanent (C) crude (D) relentless (E) incomplete

1.

PROTRACTED (A) boring (B) condensed (C) prolonged (D) comprehensive (E) measured

2.

5.

OBSEQUIOUS (A) courteous (B) fawning (C) respectful (D) overbearing (E) inexperienced

3.

ABACUS (A) casserole (B) blackboard (C) slide rule (D) adding device (E) long spear

1.

OBEISANCE (A) salary (B) justification (C) conduct (D) deference (E) forethought

6.

LOQUACIOUS (A) queer (B) logical (C) gracious (D) rural (E) voluble

4.

SEISMISM (A) inundation (B) tide (C) volcano (D) earthquake (E) tornado

2.

PEDANTIC (A) stilted (B) odd (C) footworn (D) selfish (E) sincere

3.

4.

DEPLORE (A) condone (B) forget (C) forgive (D) deny (E) regret BANAL (A) commonplace (B) flippant (C) pathetic (D) new (E) unexpected

Vocabulary Test 8

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3.

4.

5.

6.

7.

PETULANT (A) lazy (B) loving (C) patient (D) peevish (E) wary PROCLIVITY (A) backwardness (B) edict (C) rainfall (D) slope (E) tendency TRENCHANT (A) keen (B) good (C) edible (D) light (E) subterranean VAPID (A) carefree (B) crazy (C) insipid (D) spotty (E) speedy PROGNOSTICATE (A) forecast (B) ravish (C) salute (D) scoff (E) succeed


2.

INVARIABLE (A) diverse (B) eternal (C) fleeting (D) inescapable (E) uniform VORACIOUS (A) excitable (B) honest (C) greedy (D) inclusive (E) circular

3.

CONCENTRATE (A) agitate (B) protest (C) debate (D) harden (E) consolidate

4.

PLAGIARIZE (A) annoy (B) borrow (C) steal ideas (D) imitate poorly (E) impede

5.

CORTEGE (A) advisers (B) official papers (C) slaves (D) retinue (E) personal effects

6.

9.

10.

FINITE (A) impure (B) firm (C) minute (D) limited (E) unbounded ANARCHY (A) laissez-faire (B) motor-mindedness (C) pacifism (D) lawless confusion (E) self-sufficiency


DISCRIMINATION (A) acquittal (B) insight (C) caution (D) indescretion (E) distortion

2.

INVECTIVE (A) richness (B) goal (C) solemn oath (D) praise (E) verbal abuse

3.

ADROIT (A) hostile (B) serene (C) pompous (D) skillful (E) allergic

ANTIPATHY (A) sympathy (B) detachment (C) aversion (D) amazement (E) opposition

4.

DISTRESS (A) injury (B) contortion (C) suffering (D) convulsion (E) aggravation

8.

PROPRIETY (A) advancement (B) atonement (C) fitness (D) sobriety (E) use

9.

PULCHRITUDE (A) beauty (B) character (C) generosity (D) intelligence (E) wickedness

7.

DEMUR (A) object (B) agree (C) murmur (D) discard (E) consider

5.

DILETTANTE (A) epicure (B) dabbler (C) procrastinator (D) literary genius (E) playboy

10.

SCRUPULOUS (A) drunken (B) ill (C) masterful (D) exact (E) stony

8.

PARAGON (A) dummy (B) lover (C) image (D) model (E) favorite

6.

PROVISIONAL (A) military (B) tentative (C) absentee (D) democratic (E) appointed

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7.

CONDIMENT (A) ledger (B) ore (C) telegraph device (D) musical instrument (E) spice

5.

ASTUTE (A) shrewd (B) futile (C) potent (D) provocative (E) ruthless

8.

RECALCITRANT (A) insincere (B) obstinate (C) crafty (D) conservative (E) reconcilable

6.

PROVISO (A) final treaty (B) condition (C) demand (D) official document (E) proclamation

9.

BON MOT (A) witticism (B) pun (C) praise (D) last word (E) exact meaning

7.

MACABRE (A) gruesome (B) meager (C) sordid (D) fantastic (E) cringing

ACCOUTREMENTS (A) sealed orders (B) equipment (C) cartons (D) correspondence (E) financial records

8.

AUGMENT (A) curtail (B) change (C) restore (D) conceal (E) increase

Vocabulary Test 11

9.

10.

1.

2.

HYPOTHESIS (A) assumption (B) proof (C) estimate (D) random guess (E) established truth ALACRITY (A) slowness (B) indecision (C) caution (D) promptness (E) fearlessness

10.

INTEGRAL (A) useful (B) powerful (C) essential (D) mathematical (E) indestructible IMPUNITY (A) shamelessness (B) power of action (C) self-reliance (D) haughtiness (E) exemption from punishment

3.

BELLICOSE (A) boastful (B) warlike (C) sluggish (D) fantastic (E) oriental

4.

ARROYO (A) cliff (B) plain (C) ranch (D) gully (E) cactus

5.

AUGUR (A) enrage (B) foretell (C) suggest (D) evaluate (E) minimize

6.

CONTRITE (A) infectious (B) worried (C) penitent (D) sympathetic (E) tolerant

7.

PETULANT (A) silly (B) gay (C) sarcastic (D) officious (E) quarrelsome

8.

PAEAN (A) prize (B) song of praise (C) decoration (D) certificate (E) story of heroism

9.

EXOTIC (A) romantic (B) exciting (C) wealthy (D) strange (E) tropical

Vocabulary Test 12

3.

JETTISON (A) throw overboard (B) dismantle (C) scuttle (D) unload cargo (E) camouflage

1.

LATENT (A) inherent (B) lazy (C) dormant (D) crushed (E) anticipated

4.

VACILLATE (A) glitter (B) swerve (C) surrender (D) soften (E) waver

2.

OBDURATE (A) patient (B) stupid (C) rude (D) stubborn (E) tolerant

10.

ARCHIPELAGO (A) slender isthmus (B) long, narrow land mass (C) string of lakes (D) high, flat plain (E) group of small islands

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2.

PREVARICATE (A) hesitate (B) lie (C) protest (D) ramble (E) remain silent INCREDULOUS (A) argumentative (B) imaginative (C) indifferent (D) irreligious (E) skeptical

9.

EFFRONTERY (A) bad taste (B) conceit (C) dishonesty (D) impudence (E) snobbishness

7.

GLIB (A) cheerful (B) delightful (C) dull (D) fluent (E) gloomy

10.

ACQUIESCENCE (A) advice (B) advocacy (C) compliance (D) friendliness (E) opposition

8.

PAUCITY (A) abundance (B) ease (C) hardship (D) lack (E) stoppage

9.

LUCRATIVE (A) debasing (B) fortunate (C) influential (D) monetary (E) profitable

Vocabulary Test 14

PLACATE (A) amuse (B) appease (C) embroil (D) pity (E) reject

1.

COGNIZANT (A) afraid (B) aware (C) capable (D) ignorant (E) optimistic

2.

5.

DISSONANCE (A) disapproval (B) disaster (C) discord (D) disparity (E) dissimilarity

3.

PSEUDO (A) deep (B) obvious (C) pretended (D) provoking (E) spiritual

1.

CONNIVANCE (A) approval (B) collusion (C) conflict (D) permission (E) theft

6.

IMMINENT (A) declining (B) distinguished (C) impending (D) terrifying (E) unlikely

4.

FLOTSAM (A) dark sand (B) fleet (C) life preserver (D) shoreline (E) wreckage

2.

SAVANT (A) diplomat (B) inventor (C) learned man (D) thrifty person (E) wiseacre

7.

TORSION (A) bending (B) compressing (C) sliding (D) stretching (E) twisting

5.

AWRY (A) askew (B) deplorable (C) odd (D) simple (E) striking

3.

INCIPIENT (A) beginning (B) dangerous (C) hasty (D) secret (E) widespread

8.

ACCRUED (A) added (B) incidental (C) miscellaneous (D) special (E) unearned

6.

NEFARIOUS (A) clever (B) necessary (C) negligent (D) short-sighted (E) wicked

4.

VIRILE (A) honest (B) loyal (C) manly (D) pugnacious (E) virtuous

3.

4.

RETICENT (A) fidgety (B) repetitious (C) reserved (D) restful (E) truthful STIPULATE (A) bargain (B) instigate (C) prefer (D) request (E) specify

10.

INDUBITABLE (A) doubtful (B) fraudulent (C) honorable (D) safe (E) undeniable

Vocabulary Test 15

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5.

6.

7.

8.

9.

10.

ASSIDUOUS (A) courteous (B) diligent (C) discouraged (D) frank (E) slow CATACLYSM (A) blunder (B) superstition (C) treachery (D) triumph (E) upheaval AUSPICIOUS (A) condemnatory (B) conspicuous (C) favorable (D) questionable (E) spicy SATIRE (A) conversation (B) criticism (C) gossip (D) irony (E) jesting VERNACULAR (A) common speech (B) correct usage (C) long words (D) oratory (E) poetic style EMOLUMENT (A) capital (B) compensation (C) liabilities (D) loss (E) output

3.

4.

5.

6.

7.

ETHNOLOGY (A) causation (B) morals (C) social psychology (D) study of races (E) word analysis DEDUCE (A) diminish (B) infer (C) outline (D) persuade (E) subtract PANORAMIC (A) brilliant (B) comprehensive (C) pretty (D) fluorescent (E) unique IGNOMINY (A) disgrace (B) isolation (C) misfortune (D) sorrow (E) stupidity RELEVANT (A) ingenious (B) inspiring (C) obvious (D) pertinent (E) tentative


DISPARAGE (A) belittle (B) upgrade (C) erase (D) reform (E) scatter

2.

LIMPID (A) calm (B) clear (C) crippled (D) delightful (E) opaque

3.

DERISIVE (A) dividing (B) furnishing (C) reflecting (D) expressing ridicule (E) suggesting

4.

DEBILITATE (A) encourage (B) insinuate (C) prepare (D) turn away (E) weaken

5.

OPULENT (A) fearful (B) free (C) oversized (D) trustful (E) wealthy

6.

BLANDISHMENT (A) dislike (B) flattery (C) ostentation (D) praise (E) rejection

8.

GAMUT (A) game (B) range (C) risk (D) organization (E) plan

9.

APPOSITE (A) appropriate (B) contrary (C) different (D) spontaneous (E) tricky

7.

CRYPTIC (A) appealing (B) arched (C) deathly (D) hidden (E) intricate

AMBULATORY (A) able to walk (B) confined to bed (C) injured (D) quarantined (E) suffering from disease

8.

RAUCOUS (A) harsh (B) loud (C) querulous (D) rational (E) violent


TURGID (A) dusty (B) muddy (C) rolling (D) swollen (E) tense

2.

EXPUNGE (A) clarify (B) copy (C) delete (D) investigate (E) underline

10.

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9.

AVIDITY (A) friendliness (B) greediness (C) resentment (D) speed (E) thirst

7.

RECOMPENSE (A) approval (B) blessing (C) gift (D) prayer (E) reward

5.

TRUNCHEON (A) baton (B) canopy (C) dish (D) gun (E) rejected food

10.

EPITOME (A) conclusion (B) effort (C) letter (D) summary (E) summit

8.

BEATIFIC (A) giving bliss (B) eager (C) hesitant (D) lovely (E) sad

6.

SEBACEOUS (A) fatty (B) fluid (C) porous (D) transparent (E) watery

9.

SANGUINE (A) limp (B) mechanical (C) muddy (D) red (E) stealthy

7.

DILATORY (A) hairy (B) happy-go-lucky (C) ruined (D) tardy (E) well-to-do

10.

SURCEASE (A) end (B) hope (C) resignation (D) sleep (E) sweetness

8.

EBULLITION (A) bathing (B) boiling (C) refilling (D) retiring (E) returning

Vocabulary Test 19

9.

RELEGATE (A) banish (B) deprive (C) designate (D) report (E) request


2.

HIATUS (A) branch (B) disease (C) gaiety (D) insect (E) break PLENARY (A) easy (B) empty (C) full (D) rewarding (E) untrustworthy CAPRICIOUS (A) active (B) fickle (C) opposed (D) sheeplike (E) slippery

1.

SPECIOUS (A) frank (B) particular (C) deceptive (D) suspicious (E) vigorous

2.

5.

EXTIRPATE (A) besmirch (B) clean (C) eradicate (D) favor (E) subdivide

3.

PERUSE (A) endure (B) perpetuate (C) read (D) undertake (E) urge

1.

REDOLENT (A) odorous (B) quick (C) refined (D) repulsive (E) supple

6.

EQUIVOCAL (A) doubtful (B) medium (C) monotonous (D) musical (E) well-balanced

4.

RANCOR (A) dignity (B) fierceness (C) odor (D) spite (E) suspicion

2.

DISSIMULATE (A) confound (B) pretend (C) question (D) separate (E) strain

3.

4.

SENTIENT (A) very emotional (B) capable of feeling (C) hostile (D) sympathetic (E) wise OBVIATE (A) grasp (B) reform (C) simplify (D) smooth (E) make unnecessary

10.

RECONDITE (A) brittle (B) concealed (C) explored (D) exposed (E) uninformed

Vocabulary Test 20

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3.

4.

5.

6.

7.

SUBLIME (A) below par (B) highly praised (C) extreme (D) noble (E) settled VIXEN (A) fever (B) quarrelsome woman (C) sea bird (D) sedative (E) squirrel SEDULOUS (A) deceptive (B) diligent (C) grassy (D) hateful (E) sweet VITIATE (A) contaminate (B) flavor (C) freshen (D) illuminate (E) refer CURVET (A) come around (B) follow (C) leap (D) restrain (E) warp


2.

ADULATION (A) approach (B) echo (C) flattery (D) gift (E) imitation SUBSEQUENTLY (A) continually (B) factually (C) farther (D) incidentally (E) later

3.

EXPURGATE (A) amplify (B) emphasize (C) offend (D) purify (E) renew

4.

LIAISON (A) derivative (B) liability (C) link (D) malice (E) officer

5.

SEDENTARY (A) careful (B) inactive (C) notched (D) pleasant (E) uneventful

6.

9.

CONSUMMATE (A) achieve (B) devour (C) effuse (D) ignite (E) take

10.

MUNIFICENTLY (A) acutely (B) awkwardly (C) cruelly (D) generously (E) militarily


LUGUBRIOUS (A) calm (B) doleful (C) tepid (D) wan (E) warm

2.

DISCONSOLATE (A) desolate (B) emotional (C) incorrigible (D) gloomy (E) sad

3.

COTERIE (A) clique (B) cure-all (C) expert judge (D) forerunner (E) society girl

LASSITUDE (A) childishness (B) energy (C) ignorance (D) languor (E) seriousness

4.

CONDUIT (A) doorway (B) electric generator (C) power (D) screen (E) tube

8.

ADVENTITIOUS (A) accidental (B) courageous (C) favorable (D) risk taking (E) expected

9.

ANIMUS (A) animosity (B) breath (C) faith (D) light (E) poison

7.

ALTRUISTICALLY (A) egotistically (B) harmfully (C) harshly (D) highly (E) unselfishly

5.

SHIBBOLETH (A) a friend in need (B) lonely home (C) personal complaint (D) reason for action (E) watchword

10.

DESCRIED (A) hailed (B) rebuffed (C) recalled (D) regretted (E) sighted

8.

PERFIDIOUS (A) ambiguous (B) flawless (C) perforated (D) treacherous (E) trusting

6.

EVANESCENT (A) colorful (B) consecrated (C) converted (D) empty (E) vanishing

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7.

PARSIMONIOUS (A) cautious (B) ecclesiastical (C) luxurious (D) stingy (E) unique

5.

KEN (A) acceptance (B) belief (C) dune (D) knowledge (E) woody glen

8.

MACHIAVELLIAN (A) cunning (B) humble (C) kingly (D) machine-like (E) saintly

6.

GERMANE (A) diseased (B) foreign (C) infected (D) pertinent (E) polished

9.

COMPENDIUM (A) amplification (B) appendix (C) expansion (D) paraphrase (E) summary

7.

VITUPERATION (A) abuse (B) appendectomy (C) complication (D) rejuvenation (E) repeal

MEGALOMANIA (A) desire for beauty (B) mania for sympathy (C) miserliness (D) passion for grandeur (E) pity for the poor

8.

CHIMERICAL (A) clever (B) imaginary (C) experimental (D) foreign (E) provisional

10.


2.

TORPOR (A) cyclone (B) frenzy (C) sluggishness (D) strain (E) twisting ESOTERIC (A) clear (B) external (C) popular (D) secret (E) uncertain

9.

10.

DULCIMER (A) dolly (B) doublet (C) duenna (D) gadget (E) musical instrument SARTORIAL (A) disheveled (B) frozen (C) satirical (D) tailored (E) warm

3.

CONDIGN (A) deserved (B) hidden (C) perplexed (D) pretended (E) unworthy

4.

EPHEMERALLY (A) enduringly (B) lightly (C) openly (D) suspiciously (E) transiently

5.

HISTRIONIC (A) authentic (B) hysterical (C) reportorial (D) sibilant (E) theatrical

6.

URBANITY (A) aggressiveness (B) mercenary (C) municipality (D) rustic (E) suavity

7.

TRUCULENT (A) rambling (B) relenting (C) savage (D) tranquil (E) weary

8.

INVEIGH (A) allure (B) entice (C) guide cautiously (D) originate (E) speak bitterly

9.

DESULTORY (A) delaying (B) disconnected (C) flagrant (D) insulting (E) irritating

Vocabulary Test 24

3.

SUPERCILIOUSLY (A) critically (B) disdainfully (C) hypersensitively (D) naïvely (E) softly

1.

VERTIGO (A) curiosity (B) dizziness (C) enlivenment (D) greenness (E) invigoration

4.

ABSTEMIOUS (A) blatant (B) exhilarating (C) greedy (D) temperate (E) wasteful

2.

DEBACLE (A) ceremony (B) collapse (C) dance (D) deficit (E) dispute

10.

INGENUOUS (A) clever (B) naïve (C) ignorant (D) native (E) unkind

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2.

3.

CUMULATIVE (A) additive (B) clumsy (C) cumbersome (D) incorrect (E) secretive EPIGRAM (A) chemical term (B) exclamation (C) outer skin (D) pithy saying (E) tombstone GESTICULATE (A) dance (B) digest easily (C) ridicule (D) travel (E) use gestures

4.

BEGUILE (A) benefit (B) bind (C) deceive (D) envy (E) petition

5.

AVID (A) eager (B) glowing (C) indifferent (D) lax (E) potent

6.

9.

10.

BEREFT (A) annoyed (B) awarded (C) deprived (D) enraged (E) insane

7.

PALLIATIVE (A) boring (B) callous (C) permanent (D) softening (E) unyielding

ELUCIDATE (A) condense (B) escape (C) evade (D) explain (E) shine through

8.

FOMENT (A) curb (B) explode (C) exclude (D) turn into wine (E) instigate

9.

PREDACIOUS (A) beautiful (B) incongruous (C) peaceful (D) preying (E) valuable


2.

EMOLLIENT (A) comical (B) despicable (C) enthusiastic (D) raucous (E) soothing NOSTALGIC (A) expressive (B) forgetful (C) homesick (D) inconstant (E) seasick

10.

RESILIENT (A) thrifty (B) elastic (C) timid (D) fragile (E) unsociable

Vocabulary Test 27

3.

EXPIATE (A) atone for (B) die (C) hasten (D) imitate (E) make holy

1.

BLATANT (A) clamorous (B) conceited (C) prudish (D) reticent (E) unsuited

LABYRINTH (A) laboratory (B) maze (C) path (D) portal (E) room

4.

PARADOX (A) accepted opinion (B) axiom (C) contradiction (D) enigma (E) pattern

2.

ADVERSITY (A) advertising (B) counsel (C) criticism (D) misfortune (E) proficiency

7.

REGURGITATE (A) make new investments (B) obliterate (C) restore to solvency (D) slacken (E) surge back

5.

ARCHETYPE (A) bowman (B) original model (C) public records (D) roguishness (E) star

3.

CADAVEROUS (A) cheerful (B) contemptible (C) ghastly (D) hungry (E) ill-bred

8.

PODIUM (A) chemical element (B) dais (C) foot specialist (D) magistrate (E) Roman infantryman

6.

MUNDANE (A) deformed (B) free (C) rough-shelled (D) tearful (E) worldly

4.

WRAITH (A) anger (B) apparition (C) figurine (D) mannequin (E) model

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5.

6.

7.

8.

9.

10.

PERSPICACITY (A) clearness (B) dullness (C) keenness (D) vastness (E) wideness EXTRANEOUS (A) derived (B) foreign (C) unsuitable (D) visible (E) wasteful PAROXYSM (A) catastrophe (B) sudden outburst (C) illusion (D) lack of harmony (E) loss of all bodily movement SAPIENT (A) discerning (B) foolish (C) mocking (D) soapy (E) youthful FLACCID (A) flabby (B) golden (C) hard (D) strong (E) wiry IMPECUNIOUS (A) frugal (B) guiltless (C) miserly (D) monied (E) poor

3.

4.

5.

6.

7.

MUTINOUS (A) silent (B) oceangoing (C) rebellious (D) miserable (E) deaf NEGLIGENT (A) lax (B) desperate (C) cowardly (D) ambitious (E) informal CONTEST (A) disturb (B) dispute (C) detain (D) distrust (E) contain QUERY (A) wait (B) lose (C) show (D) ask (E) demand INSIDIOUS (A) treacherous (B) excitable (C) internal (D) distracting (E) secretive


CALLIGRAPHY (A) weaving (B) handwriting (C) drafting (D) mapmaking (E) graph making

2.

SYNCHRONIZE (A) happen at the same time (B) follow immediately in time (C) alternate between events (D) postpone to a future time (E) have difficulty in hearing

3.

SEMBLANCE (A) surface (B) diplomacy (C) replacement (D) appearance (E) confidence

4.

WISTFUL (A) winding (B) mutual (C) exciting (D) rugged (E) yearning

5.

CURTAIL (A) threaten (B) strengthen (C) lessen (D) hasten (E) collide

6.

NOXIOUS (A) spicy (B) smelly (C) foreign (D) noisy (E) harmful

8.

PALPITATE (A) mash (B) stifle (C) creak (D) pace (E) throb

9.

ANIMOSITY (A) hatred (B) interest (C) silliness (D) amusement (E) power

7.

PAUCITY (A) fatigue (B) scarcity (C) nonsense (D) waste (E) motion

EGOTISM (A) sociability (B) aggressiveness (C) self-confidence (D) conceit (E) willingness

8.

JEOPARDIZE (A) soothe (B) cleanse (C) enjoy (D) reward (E) endanger


ABDUCT (A) ruin (B) aid (C) fight (D) abolish (E) kidnap

2.

DEMERIT (A) outcome (B) fault (C) prize (D) notice (E) belief

10.

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9.

10.

INTREPID (A) exhausted (B) moderate (C) anxious (D) youthful (E) fearless

7.

AMOROUS (A) shapeless (B) helpful (C) familiar (D) loving (E) solemn

5.

CULMINATION (A) rebellion (B) lighting system (C) climax (D) destruction (E) mystery

TREACHEROUS (A) ignorant (B) envious (C) disloyal (D) cowardly (E) inconsiderate

8.

ALLEVIATE (A) reject (B) ease (C) imitate (D) consent (E) elevate

6.

INSUPERABLE (A) incomprehensible (B) elaborate (C) unusual (D) indigestible (E) unconquerable

9.

NEOPHYTE (A) participant (B) officer (C) beginner (D) winner (E) quarrel

7.

CLICHÉ (A) summary argument (B) new information (C) new hat (D) trite phrase (E) lock device

10.

SOLACE (A) comfort (B) weariness (C) direction (D) complaint (E) respect

8.

CONCESSION (A) nourishment (B) plea (C) restoration (D) similarity (E) acknowledgment

9.

INSIPID (A) disrespectful (B) uninteresting (C) persistent (D) whole (E) stimulating


2.

UNSAVORY (A) unfriendly (B) joyless (C) tactless (D) colorless (E) tasteless HEARSAY (A) testimony (B) argument (C) rumor (D) accusation (E) similarity

Vocabulary Test 31

HAMPER (A) restrain (B) pack (C) clarify (D) grip (E) err

1.

BEDLAM (A) inadequacy (B) confusion (C) translation (D) courtesy (E) curiosity

2.

5.

INFALLIBLE (A) negative (B) unfair (C) essential (D) certain (E) weary

3.

WANGLE (A) moan (B) mutilate (C) exasperate (D) manipulate (E) triumph

1.

DUBIOUS (A) economical (B) well-groomed (C) boring (D) discouraged (E) uncertain

6.

CONTEND (A) solve (B) observe (C) outwit (D) encourage (E) compete

4.

PROCUREMENT (A) acquisition (B) resolution (C) healing (D) importance (E) miracle

2.

ATROCIOUS (A) brutal (B) innocent (C) shrunken (D) yellowish (E) unsound

3.

4.

ULTIMATUM (A) shrewd plan (B) final terms (C) first defeat (D) dominant leader (E) electric motor GIRD (A) surround (B) appeal (C) request (D) break (E) glance

10.

REPRISAL (A) retaliation (B) drawing (C) capture (D) release (E) suspicion

Vocabulary Test 32

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3.

4.

5.

6.

7.

8.

PRESTIGE (A) speed (B) influence (C) omen (D) pride (E) excuse VINDICATE (A) outrage (B) waver (C) enliven (D) justify (E) fuse EXUDE (A) accuse (B) discharge (C) inflect (D) appropriate (E) distress FACTION (A) clique (B) judgment (C) truth (D) type of architecture (E) health INCLEMENT (A) merciful (B) sloping (C) harsh (D) disastrous (E) personal SPURIOUS (A) concise (B) false (C) obstinate (D) sarcastic (E) severe


2.

CONTROVERSIAL (A) faultfinding (B) pleasant (C) debatable (D) ugly (E) talkative GHASTLY (A) hasty (B) furious (C) breathless (D) deathlike (E) spiritual

3.

BELLIGERENT (A) worldly (B) warlike (C) loudmouthed (D) furious (E) artistic

4.

PROFICIENCY (A) wisdom (B) oversupply (C) expertness (D) advancement (E) sincerity

5.

COMPASSION (A) rage (B) strength of character (C) forcefulness (D) sympathy (E) uniformity

6.

DISSENSION (A) treatise (B) pretense (C) fear (D) lineage (E) discord

9.

SUBSERVIENT (A) existing (B) obsequious (C) related (D) underlying (E) useful

7.

INTIMATE (A) charm (B) hint (C) disguise (D) frighten (E) hum

10.

IMPORTUNE (A) aggrandize (B) carry (C) exaggerate (D) prolong (E) urge

8.

BERATE (A) classify (B) scold (C) underestimate (D) take one’s time (E) evaluate

9.

10.

DEARTH (A) scarcity (B) width (C) affection (D) wealth (E) warmth MEDITATE (A) rest (B) stare (C) doze (D) make peace (E) reflect


STAGNANT (A) inactive (B) alert (C) selfish (D) difficult (E) scornful

2.

MANDATORY (A) insane (B) obligatory (C) evident (D) strategic (E) unequaled

3.

INFERNAL (A) immodest (B) incomplete (C) domestic (D) second-rate (E) fiendish

4.

EXONERATE (A) free from blame (B) warn (C) drive out (D) overcharge (E) plead

5.

ARBITER (A) friend (B) judge (C) drug (D) tree surgeon (E) truant

6.

ENMITY (A) boredom (B) puzzle (C) offensive language (D) ill will (E) entanglement

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7.

DISCRIMINATE (A) fail (B) delay (C) accuse (D) distinguish (E) reject

5.

CITE (A) protest (B) depart (C) quote (D) agitate (E) perform

8.

DERISION (A) disgust (B) ridicule (C) fear (D) anger (E) heredity

6.

OBLIVION (A) hindrance (B) accident (C) courtesy (D) forgetfulness (E) old age

9.

EXULTANT (A) essential (B) elated (C) praiseworthy (D) plentiful (E) high-priced

7.

CARDINAL (A) independent (B) well-organized (C) subordinate (D) dignified (E) chief

OSTENSIBLE (A) vibrating (B) odd (C) apparent (D) standard (E) ornate

8.

DEPLETE (A) restrain (B) corrupt (C) despair (D) exhaust (E) spread out

10.


2.

ABHOR (A) hate (B) admire (C) taste (D) skip (E) resign DUTIFUL (A) lasting (B) sluggish (C) required (D) soothing (E) obedient

9.

10.

SUPERSEDE (A) retire (B) replace (C) overflow (D) bless (E) oversee SPORADIC (A) bad-tempered (B) infrequent (C) radical (D) reckless (E) humble

3.

DIMINUTIVE (A) proud (B) slow (C) small (D) watery (E) puzzling

4.

PLIGHT (A) departure (B) weight (C) conspiracy (D) predicament (E) stamp

5.

ILLICIT (A) unlawful (B) overpowering (C) ill-advised (D) small-scale (E) unreadable

6.

BENIGN (A) contagious (B) fatal (C) ignorant (D) kindly (E) decorative

7.

REVERIE (A) abusive language (B) love song (C) backward step (D) daydream (E) holy man

8.

APPREHENSIVE (A) quiet (B) firm (C) curious (D) sincere (E) fearful

9.

RECOIL (A) shrink (B) attract (C) electrify (D) adjust (E) enroll

Vocabulary Test 36

3.

ZEALOT (A) breeze (B) enthusiast (C) vault (D) wild animal (E) musical instrument

1.

NEUTRALIZE (A) entangle (B) strengthen (C) counteract (D) combat (E) converse

4.

MAGNANIMOUS (A) high-minded (B) faithful (C) concerned (D) individual (E) small

2.

INSINUATE (A) destroy (B) hint (C) do wrong (D) accuse (E) release

10.

GUISE (A) trickery (B) request (C) innocence (D) misdeed (E) appearance

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2.

3.

ACQUIT (A) increase (B) harden (C) clear (D) sharpen (E) sentence DEXTERITY (A) conceit (B) skill (C) insistence (D) embarrassment (E) guidance ASSIMILATE (A) absorb (B) imitate (C) maintain (D) outrun (E) curb

4.

DESPONDENCY (A) relief (B) gratitude (C) dejection (D) hatred (E) poverty

5.

BUOYANT (A) conceited (B) cautioning (C) youthful (D) musical (E) cheerful

6.

PUGNACIOUS (A) sticky (B) cowardly (C) precise (D) vigorous (E) quarrelsome

7.

LOATH (A) idle (B) worried (C) unwilling (D) ready (E) sad

ABSCOND (A) detest (B) reduce (C) swallow up (D) dismiss (E) flee

8.

INVENTIVE (A) aimless (B) clever (C) moist (D) false (E) nearby

Vocabulary Test 38

9.

LITHE (A) tough (B) obstinate (C) flexible (D) damp (E) gay

10.

VACILLATE (A) waver (B) defeat (C) favor (D) endanger (E) humiliate

9.

10.

1.

2.

BOUNTY (A) limit (B) boastfulness (C) cheerfulness (D) reward (E) punishment NOVICE (A) storyteller (B) iceberg (C) adolescent (D) mythical creature (E) beginner

Vocabulary Test 39

3.

BOLSTER (A) contradict (B) insist (C) defy (D) sleep (E) prop

1.

OBNOXIOUS (A) dreamy (B) visible (C) angry (D) daring (E) objectionable

CULINARY (A) having to do with cooking (B) pertaining to dressmaking (C) fond of eating (D) loving money (E) tending to be secretive

4.

MOBILE (A) changeable (B) scornful (C) mechanical (D) stylish (E) solid

2.

VERBATIM (A) word for word (B) at will (C) without fail (D) in secret (E) in summary

7.

CAPRICE (A) wisdom (B) ornament (C) pillar (D) whim (E) energy

5.

CREDULITY (A) prize (B) feebleness (C) balance (D) laziness (E) belief

3.

ENTICE (A) inform (B) observe (C) permit (D) attract (E) disobey

8.

DETERRENT (A) restraining (B) cleansing (C) deciding (D) concluding (E) crumbling

6.

DOLDRUMS (A) charity (B) curing agents (C) contagious disease (D) low spirits (E) places of safety

4.

ACCLAIM (A) discharge (B) excel (C) applaud (D) divide (E) speed

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5.

6.

7.

8.

9.

10.

TURBULENCE (A) treachery (B) commotion (C) fear (D) triumph (E) overflow DEFER (A) discourage (B) postpone (C) empty (D) minimize (E) estimate ADAGE (A) proverb (B) supplement (C) tool (D) youth (E) hardness ENSUE (A) compel (B) remain (C) absorb (D) plead (E) follow ZENITH (A) lowest point (B) compass (C) summit (D) middle (E) wind direction HYPOTHETICAL (A) magical (B) visual (C) two-faced (D) theoretical (E) excitable

3.

4.

5.

6.

HAVOC (A) festival (B) disease (C) ruin (D) sea battle (E) luggage REJUVENATE (A) reply (B) renew (C) age (D) judge (E) reconsider STILTED (A) stiffly formal (B) talking much (C) secretive (D) fashionable (E) senseless SOLILOQUY (A) figure of speech (B) historical incident (C) monologue (D) isolated position (E) contradiction


SUPERFICIAL (A) shallow (B) unusually fine (C) proud (D) aged (E) spiritual

2.

DISPARAGE (A) separate (B) compare (C) refuse (D) belittle (E) imitate

3.

PROTAGONIST (A) prophet (B) explorer (C) talented child (D) convert (E) leading character

4.

LUDICROUS (A) profitable (B) excessive (C) disordered (D) ridiculous (E) undesirable

5.

INTREPID (A) moist (B) tolerant (C) fearless (D) rude (E) gay

6.

SAGE (A) wise man (B) tropical tree (C) tale (D) era (E) fool

7.

AFFABLE (A) monotonous (B) affected (C) wealthy (D) sociable (E) selfish

8.

NEBULOUS (A) subdued (B) eternal (C) dewy (D) cloudy (E) careless STEREOTYPED (A) lacking originality (B) illuminating (C) pictorial (D) free from disease (E) sparkling

7.

ADMONISH (A) polish (B) escape (C) worship (D) distribute (E) caution

STUPEFY (A) lie (B) talk nonsense (C) bend (D) make dull (E) overeat

8.

BESET (A) plead (B) perplex (C) pertain to (D) deny (E) deprive of


IMPROMPTU (A) offhand (B) laughable (C) fascinating (D) rehearsed (E) deceptive

9.

2.

CHIVALROUS (A) crude (B) military (C) handsome (D) foreign (E) courteous

10.

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9.

10.

FIGMENT (A) ornamental openwork (B) perfume (C) undeveloped fruit (D) statuette (E) invention

7.

CENSURE (A) erase (B) build up (C) criticize adversely (D) charm (E) help

5.

INFRINGE (A) enrage (B) expand (C) disappoint (D) weaken (E) trespass

GLIB (A) dull (B) thin (C) weak (D) fluent (E) sharp

8.

DEVIATE (A) destroy (B) lower in value (C) invent (D) stray (E) depress

6.

UNCANNY (A) ill-humored (B) immature (C) weird (D) unrestrained (E) insincere

9.

SWARTHY (A) dark-complexioned (B) slender (C) grass-covered (D) springy (E) rotating

7.

SUBMISSIVE (A) unintelligent (B) underhanded (C) destructive (D) enthusiastic (E) meek

MERCENARY (A) poisonous (B) unworthy (C) serving only for pay (D) luring by false charms (E) showing pity

8.

PEER (A) ancestor (B) teacher (C) judge (D) equal (E) assistant

9.

EULOGIZE (A) kill (B) apologize (C) glorify (D) soften (E) imitate


2.

FORTITUDE (A) wealth (B) courage (C) honesty (D) loudness (E) luck ABOLITION (A) retirement (B) disgust (C) enslavement (D) unrestricted power (E) complete destruction

10.

Vocabulary Test 43

EPITOME (A) pool (B) summary (C) formula (D) monster (E) song

1.

MAIM (A) heal (B) disable (C) outwit (D) murder (E) bury

2.

5.

CRESTFALLEN (A) haughty (B) dejected (C) fatigued (D) disfigured (E) impolite

3.

SUCCUMB (A) follow (B) help (C) respond (D) yield (E) overthrow

1.

EXHILARATION (A) animation (B) withdrawal (C) payment (D) suffocation (E) despair

6.

CUISINE (A) headdress (B) game of chance (C) leisurely voyage (D) artistry (E) style of cooking

4.

SLOTH (A) selfishness (B) hatred (C) laziness (D) misery (E) slipperiness

2.

RASPING (A) irritating (B) scolding (C) fastening (D) sighing (E) plundering

3.

4.

ACUTE (A) keen (B) bitter (C) brisk (D) genuine (E) certain CLIENTELE (A) legal body (B) customers (C) board of directors (D) servants (E) tenants

10.

INNOVATION (A) change (B) prayer (C) hint (D) restraint (E) inquiry

Vocabulary Test 44

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3.

4.

5.

6.

7.

8.

9.

10.

PROPONENT (A) spendthrift (B) rival (C) distributor (D) advocate (E) neighbor REDUNDANT (A) flooded (B) dreadful (C) aromatic (D) excessive (E) reclining BEGRUDGING (A) humid (B) envious (C) living in seclusion (D) involving a choice (E) aimless EMPATHIZE (A) cheapen (B) underestimate (C) charm (D) sympathize (E) forgive PRUDENT (A) lighthearted (B) eager (C) cautious (D) insincere (E) fast-moving OMNIVOROUS (A) devouring everything (B) many-sided (C) powerful (D) living on plants (E) all-knowing APPEND (A) rely (B) recognize (C) arrest (D) divide (E) attach STRATAGEM (A) sneak attack (B) military command (C) thin layer (D) deceptive device (E) narrow passage


2.

COLLABORATE (A) condense (B) converse (C) arrange in order (D) provide proof (E) act jointly FUTILITY (A) uselessness (B) timelessness (C) stinginess (D) happiness (E) indistinctness

3.

INTACT (A) blunt (B) fashionable (C) hidden (D) uninjured (E) attentive

4.

FERVOR (A) originality (B) justice (C) zeal (D) productivity (E) corruption

5.

UNERRING (A) modest (B) illogical (C) ghostly (D) matchless (E) unfailing

6.

9.

ACCESS (A) agreement (B) rapidity (C) welcome (D) approach (E) surplus

10.

PRUDENT (A) wise (B) overcritical (C) famous (D) dull (E) early


APPEASE (A) attack (B) soothe (C) pray for (D) estimate (E) confess

2.

RUTHLESS (A) senseless (B) sinful (C) ruddy (D) pitiless (E) degrading

3.

MUSTER (A) rebel (B) mask (C) gather (D) dampen (E) grumble

REFUTE (A) polish (B) disprove (C) throw away (D) break up (E) shut out

4.

EXECRATE (A) embarrass (B) desert (C) omit (D) curse (E) resign

7.

CONSENSUS (A) steadfastness of purpose (B) general agreement (C) lack of harmony (D) informal vote (E) impressive amount

5.

KNOLL (A) elf (B) mound (C) bell (D) development (E) technique

8.

COMPLIANT (A) tangled (B) grumbling (C) self-satisfied (D) treacherous (E) submissive

6.

IRATE (A) evil (B) wandering (C) repetitious (D) colorful (E) angry

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7.

GRIMACE (A) peril (B) subtle suggestion (C) signal (D) wry face (E) impurity

5.

ELICIT (A) draw forth (B) cross out (C) run away (D) lengthen (E) revise

8.

ACME (A) layer (B) summit (C) edge (D) pit (E) interval

6.

JUDICIOUS (A) wise (B) dignified (C) lighthearted (D) confused (E) respectful

9.

COVENANT (A) solemn agreement (B) formal invitation (C) religious ceremony (D) general pardon (E) hiding place

7.

UNSCATHED (A) unashamed (B) uninjured (C) unskilled (D) unsuccessful (E) unconscious

APPALL (A) honor (B) decorate (C) calm (D) bore (E) dismay

8.

CHIDE (A) misbehave (B) cool (C) select (D) conceal (E) scold

10.


2.

INCUR (A) take to heart (B) anticipate (C) bring down on oneself (D) impress by repetition (E) attack CAUSTIC (A) solemn (B) puzzling (C) biting (D) influential (E) attentive

9.

10.

CHARLATAN (A) scholar (B) acrobat (C) quack (D) faithful servant (E) fast talker DISBURSE (A) remove forcibly (B) twist (C) amuse (D) vary slightly (E) pay out

3.

FIDELITY (A) happiness (B) bravery (C) prosperity (D) hardness (E) loyalty

4.

DIFFUSE (A) explain (B) scatter (C) differ (D) congeal (E) dart

5.

AGGRESSIVE (A) disgusting (B) impulsive (C) shortsighted (D) coarse-grained (E) self-assertive

6.

AMASS (A) accumulate (B) encourage (C) comprehend (D) blend (E) astonish

7.

DIABOLIC (A) puzzling (B) uneducated (C) ornamental (D) fiendish (E) spinning

8.

FORBEARANCE (A) rejection (B) forgetfulness (C) sensitivity (D) patience (E) expectation TAINT (A) snarl (B) infect (C) unite (D) annoy (E) list

Vocabulary Test 48

3.

DILATE (A) retard (B) fade (C) wander (D) expand (E) startle

1.

PARAMOUNT (A) equal (B) supreme (C) well-known (D) difficult (E) ready

9.

4.

APATHY (A) fixed dislike (B) skill (C) sorrow (D) lack of feeling (E) discontent

2.

BROCHURE (A) heavy shoe (B) weapon (C) pamphlet (D) trite remark (E) ornament

10.

DISGRUNTLED (A) untidy (B) rambling (C) disabled (D) cheating (E) displeased

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2.

PLACID (A) apparent (B) peaceful (C) wicked (D) unusual (E) absent-minded EVASIVE (A) emotional (B) effective (C) destructive (D) empty (E) shifty

9.

LEVITY (A) cleanness (B) tastiness (C) deadliness (D) sluggishness (E) lightness

7.

OSTENTATIOUS (A) unruly (B) showy (C) varied (D) scandalous (E) probable

10.

EXCRUCIATING (A) disciplinary (B) screaming (C) torturing (D) offensive (E) outpouring

8.

CONCLAVE (A) private meeting (B) covered passage (C) solemn vow (D) curved surface (E) ornamental vase

9.

FRAY (A) combat (B) trickery (C) unreality (D) madness (E) freedom

Vocabulary Test 50

CHAOS (A) complete disorder (B) deep gorge (C) challenge (D) sudden attack (E) rejoicing

1.

DESPICABLE (A) insulting (B) ungrateful (C) contemptible (D) unbearable (E) jealous

2.

5.

DERIDE (A) question (B) ignore (C) mock (D) unseat (E) produce

3.

ARCHIVES (A) public records (B) models (C) supporting columns (D) tombs (E) large ships

1.

CHAFE (A) pretend (B) joke (C) drink deeply (D) irritate (E) lose courage

6.

ELUDE (A) gladden (B) fascinate (C) mention (D) escape (E) ignore

4.

INFAMY (A) anger (B) truth (C) disgrace (D) weakness (E) excitement

2.

MISCONSTRUE (A) hate (B) destroy (C) misbehave (D) misinterpret (E) misplace

7.

MUTABLE (A) colorless (B) harmful (C) uniform (D) changeable (E) invisible

5.

IMPINGE (A) swear (B) involve (C) erase (D) encroach (E) beg

3.

PHILANTHROPIST (A) student of language (B) collector of stamps (C) lover of mankind (D) seeker of truth (E) enemy of culture

8.

INDICATIVE (A) suggestive (B) curious (C) active (D) angry (E) certain

6.

DEPOSE (A) lay bare (B) deprive of office (C) empty (D) behead (E) blemish

4.

CASTE (A) feudal system (B) division of society (C) political theory (D) method of punishment (E) monetary system

3.

4.

PRECEPT (A) rule (B) disguise (C) refinement (D) hasty decision (E) delaying action HOMOGENEOUS (A) numerous (B) healthful (C) similar (D) assorted (E) educational

10.

OBSESS (A) fatten (B) beset (C) make dull (D) exaggerate (E) interfere

Vocabulary Test 51

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5.

6.

7.

8.

9.

10.

CHASTEN (A) punish (B) engrave (C) attract (D) trick (E) laugh at CONDUCIVE (A) pardonable (B) identical (C) incidental (D) helpful (E) exceptional SUBORDINATE (A) hostile (B) inferior (C) separate (D) earlier (E) adaptable SUPERFLUOUS (A) inexact (B) excessive (C) insincere (D) excellent (E) unreal WIELD (A) protect (B) handle (C) postpone (D) resign (E) unite GARISH (A) showy (B) talkative (C) sleepy (D) thin (E) vine-covered

3.

4.

5.

6.

MALIGN (A) slander (B) prophesy (C) entreat (D) approve (E) praise IMPOTENT (A) unwise (B) lacking strength (C) free of sin (D) without shame (E) commanding SNIVEL (A) crawl (B) cut short (C) whine (D) doze (E) giggle SOJOURN (A) court order (B) nickname (C) temporary stay (D) slip of the tongue (E) makeshift


EQUITABLE (A) charitable (B) even-tempered (C) two-faced (D) undecided (E) just

2.

AFFRONT (A) quarrel (B) fright (C) denial (D) boast (E) insult

3.

EPOCH (A) heroic deed (B) legend (C) witty saying (D) period of time (E) summary

4.

RETRIBUTION (A) donation (B) jealousy (C) intense emotion (D) slow withdrawal (E) punishment

5.

ABASE (A) forgive (B) degrade (C) attach (D) take leave (E) cut off

6.

CAREEN (A) celebrate (B) mourn (C) ridicule (D) lurch (E) beckon

7.

PLATITUDE (A) home remedy (B) trite remark (C) balance wheel (D) rare animal (E) protective film

8.

CONCORD (A) brevity (B) blame (C) kindness (D) worry (E) agreement ABOMINABLE (A) hateful (B) ridiculous (C) untamed (D) mysterious (E) boastful

7.

CONVIVIAL (A) formal (B) gay (C) rotating (D) well-informed (E) insulting

QUALM (A) sudden misgiving (B) irritation (C) cooling drink (D) deceit (E) attention to detail

8.

RAMPANT (A) playful (B) crumbling (C) roundabout (D) unchecked (E) defensive


MEANDER (A) grumble (B) wander aimlessly (C) come between (D) weigh carefully (E) sing

9.

2.

DESTITUTION (A) trickery (B) fate (C) lack of practice (D) recovery (E) extreme poverty

10.

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9.

10.

DOCILE (A) delicate (B) positive (C) dreary (D) obedient (E) melodious

7.

ECLIPSE (A) stretch (B) obscure (C) glow (D) overlook (E) insert

5.

INANIMATE (A) emotional (B) thoughtless (C) lifeless (D) inexact (E) silly

VESTIGE (A) bone (B) test (C) entrance (D) cloak (E) trace

8.

CORRELATE (A) punish (B) wrinkle (C) conspire openly (D) give additional proof (E) connect systematically

6.

CALLOUS (A) frantic (B) misinformed (C) youthful (D) impolite (E) unfeeling

9.

INFIRMITY (A) disgrace (B) unhappiness (C) rigidity (D) hesitation (E) weakness

7.

ENHANCE (A) sympathize (B) act out (C) weaken (D) make greater (E) fascinate

PALPITATE (A) faint (B) harden (C) throb (D) soothe (E) taste

8.

DISREPUTABLE (A) impolite (B) bewildered (C) debatable (D) unavailable (E) shameful

9.

SEDATE (A) sober (B) seated (C) buried (D) drugged (E) timid

10.

LUCRATIVE (A) lazy (B) coarse (C) profitable (D) brilliant (E) amusing


2.

IMPEDIMENT (A) foundation (B) conceit (C) hindrance (D) luggage (E) instrument ADHERE (A) pursue (B) control (C) arrive (D) cling (E) attend

10.

Vocabulary Test 55

COMPOSURE (A) sensitiveness (B) weariness (C) stylishness (D) hopefulness (E) calmness

1.

PROVOCATION (A) sacred vow (B) formal announcement (C) cause of irritation (D) careful management (E) expression of disgust

2.

5.

SAVORY (A) thrifty (B) wise (C) appetizing (D) warm (E) uncivilized

3.

STAMINA (A) flatness (B) clearness (C) hesitation (D) vigor (E) reliability

1.

IMPRUDENT (A) reckless (B) unexcitable (C) poor (D) domineering (E) powerless

6.

CANDID (A) hidden (B) shining (C) straightforward (D) critical (E) warmhearted

4.

FACET (A) phase (B) humor (C) story (D) discharge (E) assistance

2.

DISSENSION (A) friction (B) analysis (C) swelling (D) injury (E) slyness

3.

4.

DEBRIS (A) sadness (B) decay (C) ruins (D) landslide (E) hindrance CONSOLIDATE (A) show pity (B) strengthen (C) restrain (D) infect (E) use up

Vocabulary Test 56

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3.

4.

5.

6.

7.

DISCONCERT (A) separate (B) cripple (C) lessen (D) upset (E) dismiss RUDIMENTARY (A) discourteous (B) brutal (C) displeasing (D) elementary (E) embarrassing AUTONOMOUS (A) self-governing (B) self-important (C) self-educated (D) self-explanatory (E) self-conscious ASCERTAIN (A) hold fast (B) long for (C) declare (D) find out (E) avoid LITERAL (A) flowery (B) matter-of-fact (C) sidewise (D) well-educated (E) firsthand

8.

OSCILLATE (A) please (B) swing (C) purify (D) saturate (E) harden

9.

CONCISE (A) accurate (B) brief (C) sudden (D) similar (E) painful

10.

CONSTERNATION (A) restraint (B) close attention (C) dismay (D) self-importance (E) acknowledgment


2.

COLOSSAL (A) ancient (B) influential (C) destructive (D) dramatic (E) huge EVICT (A) summon (B) excite (C) force out (D) prove (E) draw off

3.

MISCHANCE (A) omission (B) ill luck (C) feeling of doubt (D) unlawful act (E) distrust

4.

FELON (A) criminal (B) fugitive (C) traitor (D) coward (E) loafer

5.

CENSURE (A) empty (B) criticize (C) spread out (D) take an oath (E) omit

6.

9.

10.

IMPASSE (A) command (B) stubbornness (C) crisis (D) deadlock (E) failure ABSOLVE (A) forgive (B) reduce (C) mix (D) deprive (E) detect


CUMBERSOME (A) habitual (B) clumsy (C) hasty (D) blameworthy (E) uneducated

2.

CAPTIVATE (A) charm (B) dictate terms (C) overturn (D) find fault (E) hesitate

3.

ZEALOUS (A) serious (B) speedy (C) flawless (D) necessary (E) enthusiastic

IMPLICIT (A) unquestioning (B) rude (C) relentless (D) sinful (E) daring

4.

AROMATIC (A) shining (B) precise (C) ancient (D) fragrant (E) dry

7.

SLOVENLY (A) sleepy (B) tricky (C) untidy (D) moody (E) cowardly

5.

RETROSPECT (A) careful inspection (B) reversal of form (C) review of the past (D) respect for authority (E) special attention

8.

EXTRANEOUS (A) familiar (B) unprepared (C) foreign (D) proper (E) utmost

6.

WHET (A) bleach (B) exhaust (C) harden (D) stimulate (E) question

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7.

CONTUSION (A) puzzle (B) shrinkage (C) bruise (D) uncleanness (E) fraud

5.

PROPRIETY (A) success (B) cleverness (C) nearness (D) security (E) suitability

8.

COMPATIBLE (A) eloquent (B) adequate (C) overfed (D) comfortable (E) harmonious

6.

UNWITTING (A) undignified (B) unintentional (C) slack (D) obstinate (E) unaccustomed

9.

CALLOUS (A) secretive (B) unruly (C) gloomy (D) unfeeling (E) hotheaded

7.

ATTRIBUTE (A) quality (B) tax (C) desire (D) law (E) final sum

REPUDIATE (A) reject (B) revalue (C) repay (D) forget (E) forgive

8.

SCRUPULOUS (A) scornful (B) clean (C) frightening (D) doubting (E) conscientious

10.


2.

PROLETARIAT (A) revolutionists (B) intellectuals (C) slaves (D) laboring classes (E) landowners REQUISITE (A) desirable (B) ridiculous (C) liberal (D) necessary (E) majestic

9.

10.

USURP (A) lend money (B) replace (C) murder (D) surrender (E) seize by force CESSATION (A) witnessing (B) stopping (C) strain (D) leave-taking (E) unwillingness

3.

REGIME (A) ruler (B) military unit (C) form of government (D) contagion (E) guardian

4.

LACERATED (A) unconscious (B) stitched (C) slender (D) raveled (E) mangled

5.

AMISS (A) friendly (B) faulty (C) tardy (D) central (E) purposeless

6.

INDOLENCE (A) poverty (B) laziness (C) danger (D) truth (E) attention

7.

PRECARIOUS (A) trustful (B) early (C) previous (D) cautious (E) uncertain

8.

CONNOISSEUR (A) investigator (B) government official (C) pretender (D) critical judge (E) portrait artist

9.

HILARITY (A) wittiness (B) disobedience (C) mirth (D) heedlessness (E) contentment

Vocabulary Test 60

3.

TENACIOUS (A) violent (B) given to arguing (C) slender (D) holding fast (E) menacing

1.

RESOLUTE (A) determined (B) vibrating (C) irresistible (D) elastic (E) demanding

4.

SCINTILLATE (A) whirl (B) wander (C) scorch (D) sharpen (E) sparkle

2.

CRYSTALLIZE (A) glitter (B) give definite form to (C) chill (D) sweeten (E) polish vigorously

10.

EMIT (A) overlook (B) adorn (C) discharge (D) encourage (E) stress

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2.

3.

DYNAMIC (A) specialized (B) active (C) fragile (D) magical (E) comparative ACHILLES’ HEEL (A) source of strength (B) critical test (C) hereditary curse (D) vulnerable point (E) base conduct AD LIB (A) cheerfully (B) freely (C) carefully (D) literally (E) wisely

4.

DECRY (A) baffle (B) weep (C) trap (D) belittle (E) imagine

5.

RAVAGE (A) ruin (B) tangle (C) delight (D) scold (E) crave

6.

RENDEZVOUS (A) surrender (B) appointment (C) souvenir (D) hiding place (E) mutual exchange

7.

8.

9.

10.

NUPTIAL (A) moonlike (B) blunted (C) ritualistic (D) matrimonial (E) blessed

7.

INDISCREET (A) unpopular (B) embarrassing (C) disloyal (D) unwise (E) greatly upset

BALKED (A) swindled (B) thwarted (C) enlarged (D) waved (E) punished

8.

UNWIELDY (A) stubborn (B) unhealthy (C) monotonous (D) shameful (E) clumsy

9.

ENVISAGE (A) plot (B) conceal (C) wrinkle (D) contemplate (E) sneer


2.

AD INFINITUM (A) to a limit (B) from eternity (C) occasionally (D) endlessly (E) periodically EXTRICATE (A) disentangle (B) die out (C) praise (D) purify (E) argue with

10.

INTERIM (A) go-between (B) meantime (C) mixture (D) hereafter (E) period of rest

Vocabulary Test 63

3.

SQUALID (A) dirty (B) unresponsive (C) wasteful (D) stormy (E) congested

1.

DISHEARTEN (A) shame (B) discourage (C) astound (D) disown (E) cripple

4.

COERCE (A) coincide (B) strengthen (C) accompany (D) compel (E) seek out

2.

COMPONENT (A) memorial (B) pledge (C) convenience (D) ingredient (E) similarity

SKULK (A) trail (B) shadow (C) ambush (D) lurk (E) race

5.

INTER (A) bury (B) stab (C) change (D) make peace (E) emphasize

3.

LURK (A) stagger (B) tempt (C) sneak (D) grin (E) rob

PLETHORA (A) formal farewell (B) exclusive group (C) abundance (D) conclusive argument (E) good taste

6.

CRESCENDO (A) increasing volume (B) decreasing tempo (C) abrupt ending (D) discordant note (E) musical composition

4.

GRUDGING (A) impolite (B) dirty (C) hoarse (D) alarming (E) unwilling

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5.

6.

7.

8.

9.

10.

SEMBLANCE (A) likeness (B) noise (C) foundation (D) glance (E) error NETTLE (A) irritate (B) catch (C) accuse (D) make ill (E) fade away TREMULOUS (A) slow (B) high-pitched (C) huge (D) shaking (E) spirited TERSE (A) delicate (B) nervous (C) mild (D) numb (E) concise AFFINITY (A) solemn declaration (B) indefinite amount (C) natural attraction (D) pain (E) wealth VOLATILE (A) disobedient (B) changeable (C) forceful (D) willing (E) luxurious

3.

4.

5.

6.

RATIONAL (A) resentful (B) overjoyed (C) sensible (D) reckless (E) apologetic RECLUSE (A) schemer (B) criminal (C) miser (D) adventurer (E) hermit COMPLACENCY (A) tenderness (B) admiration (C) dependence (D) unity (E) self-satisfaction MENACE (A) kill (B) threaten (C) waste (D) indicate (E) tease


CONJECTURE (A) work (B) joke (C) initiate (D) add (E) guess

2.

DAIS (A) platform (B) easy chair (C) waiting room (D) ornamental pin (E) figurehead

3.

IMPETUS (A) deadlock (B) collision (C) warning (D) wickedness (E) stimulus

4.

INTROSPECTIVE (A) lacking strength (B) practicing self-examination (C) highly critical (D) intrusive (E) lacking confidence

5.

DEIFY (A) describe (B) disobey (C) make presentable (D) worship as a god (E) challenge

6.

AGGREGATION (A) method (B) irritation (C) prize (D) collection (E) blessing

7.

DUPE (A) combine (B) reproduce (C) fool (D) grab (E) follow

8.

ABATE (A) surprise (B) desert (C) decrease (D) humiliate (E) pay for CONGENITAL (A) existing at birth (B) displaying weakness (C) related by marriage (D) overcrowded (E) unintelligent

7.

EXALTED (A) honored (B) underhanded (C) funny (D) conceited (E) secondary

INSURGENT (A) impractical (B) unbearable (C) over-hanging (D) rebellious (E) patriotic

8.

POTENTATE (A) slave (B) soldier (C) adviser (D) informer (E) ruler


HOMAGE (A) welcome (B) honor (C) cosiness (D) criticism (E) regret

9.

2.

DISPERSE (A) restore (B) spread (C) grumble (D) soak (E) spend

10.

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9.

INTIMIDATE (A) frighten (B) suggest (C) dare (D) border upon (E) befriend

7.

SHREW (A) moneylender (B) fortuneteller (C) chronic invalid (D) unruly child (E) scolding woman

5.

FLAMBOYANT (A) scandalous (B) showy (C) nonsensical (D) manly (E) temporary

10.

SARDONIC (A) decorative (B) polished (C) strange (D) fashionable (E) sarcastic

8.

STALWART (A) diseased (B) feeble (C) needy (D) sturdy (E) truthful

6.

ECCENTRICITY (A) overabundance (B) self-consciousness (C) adaptability (D) publicity (E) oddity

Vocabulary Test 66

9.

APOGEE (A) rate of ascent (B) force of gravity (C) measuring device (D) expression of regret (E) highest point

7.

VINDICTIVE (A) gloomy (B) cowardly (C) vengeful (D) cheerful (E) boastful

BANTER (A) tease playfully (B) strut boldly (C) ruin (D) bend slightly (E) relieve

8.

GRAPHIC (A) vivid (B) harsh-sounding (C) free from error (D) dignified (E) pliable

9.

PLACARD (A) poster (B) souvenir (C) soothing medicine (D) exact reproduction (E) contemptuous remark

1.

2.

ELECTRIFY (A) punish (B) improve (C) thrill (D) explain (E) investigate DISCRETION (A) special privilege (B) individual judgment (C) unfair treatment (D) disagreement (E) embarrassment

10.

Vocabulary Test 67

GRAPPLE (A) dive (B) wrestle (C) handle (D) fit together (E) fondle

1.

LAUDABLE (A) brave (B) comical (C) peaceful (D) praiseworthy (E) conspicuous

2.

5.

LONGEVITY (A) wisdom (B) length of life (C) society (D) system of measure (E) loudness

3.

DILIGENT (A) hesitant (B) prosperous (C) offensive (D) industrious (E) straightforward

1.

GRANDIOSE (A) selfish (B) thankful (C) quarrelsome (D) elderly (E) impressive

6.

BLANCH (A) destroy (B) drink (C) whiten (D) feel (E) mend

4.

CONCOCT (A) devise (B) link together (C) harmonize (D) meet privately (E) sweeten

2.

INCONGRUOUS (A) indistinct (B) unsuitable (C) unimportant (D) illegal (E) inconvenient

3.

4.

REPRESS (A) sharpen (B) restrain (C) repeat (D) disgust (E) grieve BREACH (A) obstruction (B) violation (C) anticipation (D) accusation (E) decoration

10.

PUTREFY (A) scour (B) paralyze (C) rot (D) neglect (E) argue

Vocabulary Test 68

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3.

4.

5.

6.

7.

PRONE (A) disposed (B) speechless (C) tardy (D) two-edged (E) quick EMISSARY (A) rival (B) secret agent (C) master of ceremonies (D) refugee (E) clergyman INVALIDATE (A) turn inward (B) deprive of force (C) mistrust (D) support with facts (E) neglect CLEMENCY (A) purity (B) timidity (C) courage (D) simplicity (E) mildness UNSCATHED (A) uninterested (B) unsettled (C) unspoken (D) unharmed (E) unknown


2.

SOLICIT (A) request (B) worry (C) command (D) deny (E) depend PERTURB (A) pierce (B) filter (C) calculate (D) agitate (E) disregard

3.

JAUNTY (A) bored (B) envious (C) quarrelsome (D) chatty (E) lively

4.

DRIVEL (A) shrill laughter (B) foolish talk (C) untidy dress (D) waste matter (E) quaint humor

5.

FRUGAL (A) sickly (B) sparing (C) slow (D) chilled (E) frightened

6.

9.

10.

MASTICATE (A) chew (B) slaughter (C) ripen (D) enroll (E) tangle ANALOGY (A) imitation (B) research (C) calendar (D) similarity (E) disagreement


DILEMMA (A) punishment (B) division in ranks (C) ability to detect (D) perplexing choice (E) word with two meanings

2.

CELESTIAL (A) musical (B) heavenly (C) stately (D) unmarried (E) aged

3.

MILITANT (A) political (B) mighty (C) aggressive (D) peaceable (E) illegal

IOTA (A) first step (B) sacred picture (C) ornamental scroll (D) crystalline substance (E) very small quantity

4.

EMINENT (A) noted (B) moral (C) future (D) low (E) unwise

8.

RELINQUISH (A) shrink from (B) take pity on (C) yield (D) lessen (E) recall

9.

ALLAY (A) offend (B) suffer (C) resemble (D) assign (E) calm

7.

POACH (A) squander (B) trespass (C) outwit (D) bully (E) borrow

5.

PERCEIVE (A) resolve (B) observe (C) organize (D) stick in (E) copy down

10.

ANIMOSITY (A) liveliness (B) worry (C) ill will (D) regret (E) sarcasm

8.

DEFECTION (A) delay (B) slander (C) respect (D) desertion (E) exemption

6.

IDIOSYNCRASY (A) stupidity (B) virtue (C) personal peculiarity (D) foreign dialect (E) similarity

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7.

EDIFICE (A) tool (B) large building (C) garden (D) mushroom (E) set of books

5.

EMBELLISH (A) organize (B) involve (C) rob (D) beautify (E) correct

8.

SEEDY (A) dishonest (B) helpless (C) vague (D) nervous (E) shabby

6.

IMPLEMENT (A) carry out (B) fall apart (C) give freely (D) object strongly (E) praise highly

9.

SUPPLANT (A) spend (B) unite (C) recall (D) replace (E) purpose

7.

INSUBORDINATE (A) unreal (B) disobedient (C) inferior (D) unfaithful (E) unnecessary

10.

DESIST (A) loiter (B) stand (C) hurry (D) stumble (E) stop

8.

ITINERANT (A) small (B) intensive (C) repetitive (D) wandering (E) begging


2.

GIRD (A) stare (B) thresh (C) encircle (D) complain (E) perforate BIZARRE (A) charitable (B) joyous (C) flattering (D) insane (E) fantastic

9.

10.

ADVERSITY (A) misfortune (B) surprise (C) economy (D) publicity (E) warning DISSIPATE (A) explain (B) puzzle (C) rearrange (D) envy (E) waste

3.

ERRATIC (A) unpredictable (B) upright (C) well-informed (D) self-centered (E) artificial

4.

COVET (A) take for granted (B) keep secret (C) disbelieve (D) steal (E) long for

5.

VERBOSE (A) forbidden (B) expanding (C) talented (D) wordy (E) opinionated

6.

FLIPPANT (A) fishlike (B) anxious (C) frivolous (D) savage (E) shy

7.

ACCLAMATION (A) seasoning (B) applause (C) slope (D) harmony (E) collection

8.

INCITE (A) include (B) destroy (C) withdraw (D) arouse (E) perceive

9.

FINESSE (A) end (B) skill (C) habit (D) expense (E) vanity

10.

TANTALIZE (A) prevent (B) protect (C) rob (D) predict (E) torment

Vocabulary Test 72

3.

PERENNIAL (A) superior (B) unceasing (C) notable (D) short-lived (E) authoritative

1.

VALOR (A) courage (B) honesty (C) beauty (D) alertness (E) modesty

4.

PROGENITOR (A) genius (B) wastrel (C) forefather (D) magician (E) publisher

2.

DISSUADE (A) offend (B) lessen (C) advise against (D) spread out (E) separate

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2.

3.

INSOMNIA (A) boredom (B) loss of memory (C) seasickness (D) sleeplessness (E) lonesomeness FEASIBLE (A) enjoyable (B) juicy (C) regrettable (D) responsible (E) possible BLURT (A) brag (B) utter impulsively (C) challenge (D) shout angrily (E) weep noisily

4.

ALIENATE (A) advise (B) entertain (C) forgive (D) sympathize with (E) make unfriendly

5.

STARK (A) barely (B) offensively (C) uselessly (D) completely (E) artistically

6.

NONCHALANCE (A) refinement (B) foresight (C) air of indifference (D) lack of knowledge (E) lack of common sense

7.

GRIT (A) honesty (B) reverence (C) trustworthiness (D) cheerfulness (E) bravery

8.

MEDIATE (A) make changes (B) argue earnestly (C) consider carefully (D) propose hesitantly (E) reconcile differences

9.

DE FACTO (A) commercial (B) economic (C) in reality (D) unnecessary (E) the following

7.

RECIPROCATE (A) reconsider (B) refresh (C) repay (D) recall (E) reclaim

10.

IRREVOCABLE (A) unreliable (B) disrespectful (C) unforgivable (D) unalterable (E) heartless

8.

REBUFF (A) send back (B) make over (C) snub (D) defend (E) remind

Vocabulary Test 74

9.

CLANDESTINE (A) unfriendly (B) fateful (C) unified (D) secret (E) argumentative

1.

2.

ABYSMAL (A) bottomless (B) ill (C) forgetful (D) unoccupied (E) slight PREROGATIVE (A) forewarning (B) formal investigation (C) privilege (D) reputation (E) opening speech

10.

LETHARGY (A) unnatural drowsiness (B) excessive caution (C) lack of consideration (D) vice (E) foolishness

Vocabulary Test 75

3.

ILLUSTRIOUS (A) believable (B) unrewarding (C) cynical (D) decorative (E) famous

1.

ACCREDITED (A) obligated (B) approved (C) discharged (D) quickened (E) confessed

4.

INTERMINABLE (A) scanty (B) secret (C) open-faced (D) endless (E) stationary

2.

ADHERENT (A) clergyman (B) critic (C) executive (D) supporter (E) journalist

5.

FRANCHISE (A) secrecy (B) right to vote (C) imprisonment (D) free-for-all (E) avoidable tragedy

3.

WHEEDLE (A) mourn (B) coax (C) revolve (D) hesitate (E) entertain

6.

LINEAGE (A) brilliance (B) ancestry (C) narrowness (D) straightness (E) ceremony

4.

CIRCUITOUS (A) electrical (B) watery (C) roundabout (D) forbidding (E) tender

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5.

6.

7.

8.

9.

10.

DESPOT (A) murderer (B) impostor (C) invader (D) avenger (E) tyrant DETER (A) hinder (B) mistake (C) neglect (D) injure (E) restore UTILITARIAN (A) practical (B) widespread (C) inexpensive (D) praiseworthy (E) fortunate INCREDULITY (A) forgetfulness (B) faithlessness (C) immaturity (D) disbelief (E) unreality INTERDICT (A) lessen (B) separate (C) fatigue (D) permit (E) forbid TIMOROUS (A) necessary (B) expected (C) afraid (D) wild (E) brief

3.

4.

5.

6.

7.

KINDLE (A) relate (B) pass on (C) pretend (D) arouse (E) punish POMP (A) splendor (B) illness (C) hopefulness (D) apple (E) posture TINGE (A) mold (B) draw forth (C) color slightly (D) sketch (E) create RECOIL (A) steer (B) link up (C) put down (D) scrape (E) shrink back QUASH (A) creep (B) mix thoroughly (C) repeat (D) suppress completely (E) falsify


APROPOS (A) witty (B) forceful (C) nearly correct (D) richly decorated (E) to the point

2.

INIMICAL (A) speechless (B) unfriendly (C) unnecessarily rude (D) poor (E) hopelessly sad

3.

SORDID (A) biting (B) filthy (C) mysterious (D) griefstricken (E) sickly

4.

CATACLYSM (A) severe criticism (B) gorge (C) launching device (D) unconsciousness (E) violent upheaval

5.

FETTERED (A) stricken (B) scolded (C) commanded (D) confined (E) loosened

6.

VERACITY (A) endurance (B) selfishness (C) truthfulness (D) courtesy (E) thoughtfulness

8.

PALTRY (A) trivial (B) sacred (C) metallic (D) careless (E) positive

9.

IMPETUOUS (A) controlled (B) hasty (C) vigorous (D) defamatory (E) vehement

7.

REPLETE (A) filled (B) tarnished (C) golden (D) economical (E) wrecked

HARANGUE (A) unintelligible prose (B) ranting speech (C) poetic imagery (D) anonymous letter (E) heavy overcoat

8.

TREED (A) met (B) cornered (C) followed (D) searched (E) scented


BRAWN (A) boldness (B) muscular strength (C) rustiness (D) unruliness (E) protective covering

2.

STALEMATE (A) athletic contest (B) complete defeat (C) deadlock (D) storm (E) refusal to fight

10.

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9.

10.

DERISIVE (A) hereditary (B) rebellious (C) fragmentary (D) scornful (E) determined

7.

INCESSANT (A) even (B) illegal (C) dirty (D) continuous (E) loud

5.

VERBATIM (A) out loud (B) word for word (C) in set phrases (D) elegantly expressed (E) using too many words

TEMPER (A) decorate (B) annoy (C) blame (D) postpone (E) moderate

8.

PRATTLE (A) sell (B) storm (C) babble (D) explain (E) keep

6.

GRUELING (A) exhausting (B) surprising (C) insulting (D) embarrassing (E) boring

9.

PERVERSE (A) contrary (B) rhythmic (C) imaginary (D) alert (E) rich

7.

CREDIBILITY (A) freedom from prejudice (B) religious doctrine (C) capacity for belief (D) questioning attitude (E) good judgment

QUARRY (A) dispute (B) prey (C) initial (D) request (E) output

8.

APPROPRIATE (A) betray (B) compliment (C) take possession of (D) give thanks (E) draw near to

9.

EXONERATE (A) overcharge (B) lengthen (C) leave out (D) free from blame (E) serve as a model


2.

RESIDUE (A) dwelling (B) remainder (C) debt (D) sample (E) storehouse BUNGLE (A) complain (B) approach (C) live in (D) handle badly (E) talk boastfully

10.

Vocabulary Test 79

ADVOCATE (A) flatter (B) caution (C) recommend (D) take an oath (E) charge

1.

CALAMITOUS (A) disastrous (B) inexperienced (C) hard-hearted (D) scheming (E) slanderous

2.

5.

JILT (A) fill in (B) cast aside (C) move about (D) pick up (E) help forward

3.

PARADOX (A) virtuous man (B) equal rights (C) seeming contradiction (D) complicated design (E) geometric figure

1.

EFFIGY (A) representation (B) shadow (C) parade (D) ancestor (E) present

6.

FUTILE (A) violent (B) one-sided (C) weary (D) stingy (E) useless

4.

DISPEL (A) punish (B) excite (C) pay out (D) drive away (E) misunderstand

2.

ZEST (A) operation (B) mood (C) great dismay (D) keen enjoyment (E) false alarm

3.

4.

PATERNAL (A) generous (B) aged (C) fatherly (D) thrifty (E) narrowminded CALIBER (A) gaiety (B) quality (C) hope (D) similarity (E) politeness

10.

BLAND (A) flattering (B) foolish (C) successful (D) soothing (E) sharp

Vocabulary Test 80

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3.

4.

5.

6.

7.

ASTUTE (A) shrewd (B) inflammable (C) defiant (D) out of tune (E) bitter DISCREPANCY (A) variance (B) disbelief (C) feebleness (D) insult (E) forcefulness COPIOUS (A) copyrighted (B) tricky (C) abundant (D) complete (E) sincere ADVENT (A) approval (B) opportunity (C) welcome (D) recommendation (E) arrival IMMINENT (A) about to occur (B) never-ending (C) up-to-date (D) inconvenient (E) youthful


2.

HEEDLESS (A) unfortunate (B) expensive (C) careless (D) happy (E) weatherbeaten IMPEDIMENT (A) obstacle (B) base (C) spice (D) mechanism (E) footstool

3.

QUAVER (A) launch (B) quicken (C) sharpen (D) tremble (E) forget

4.

SHACKLE (A) hide (B) glide (C) anger (D) quiet (E) hamper

5.

LOWLY (A) idle (B) silent (C) humble (D) sorrowful (E) solitary

6.

CUBICLE (A) wedge (B) puzzle (C) tiny amount (D) unit of measure (E) small compartment

9.

PROFOUND (A) plentiful (B) beneficial (C) lengthy (D) religious (E) deep

10.

WAN (A) pale (B) humorous (C) pleasing (D) watchful (E) lovesick


HAUNT (A) contain (B) give up (C) expect (D) stay around (E) extend greatly

2.

UNMINDFUL (A) unaware (B) illogical (C) unaccustomed (D) unchanging (E) inefficient

3.

EMANCIPATE (A) change (B) overjoy (C) bring forward (D) raise up (E) set free

4.

LOLL (A) find (B) respect (C) lounge (D) steal (E) trap

8.

RANKLE (A) spread around (B) seize quickly (C) crease (D) search (E) irritate deeply

9.

INJUNCTION (A) exclamation (B) rebellion (C) directive (D) crisis (E) illegality

7.

ARRAIGN (A) debate (B) accuse (C) excite (D) cancel (E) protect

5.

SUBSEQUENT (A) later (B) lower (C) thick (D) secret (E) light

10.

DEFT (A) critical (B) conceited (C) lighthearted (D) skillful (E) tactful

8.

OBLIVIOUS (A) unwanted (B) disorderly (C) unaware (D) sickly (E) evident

6.

CRUCIAL (A) reverent (B) decisive (C) tiresome (D) dangerous (E) rude

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7.

REBUKE (A) prove (B) dislike (C) overwork (D) swallow (E) criticize

5.

EFFRONTERY (A) boldness (B) agitation (C) brilliance (D) toil (E) talkativeness

8.

CLOISTERED (A) uneasy (B) agreeable (C) sincere (D) regretful (E) confined

6.

EMBROIL (A) explain (B) entangle (C) swindle (D) greet (E) imitate

9.

DRONE (A) beggar (B) nightmare (C) queen bee (D) humming sound (E) delaying action

7.

INCANDESCENT (A) insincere (B) melodious (C) electrical (D) magical (E) glowing

PEDESTRIAN (A) clumsy (B) senseless (C) curious (D) learned (E) commonplace

8.

STENTORIAN (A) extremely careful (B) little known (C) hardly capable (D) rarely reliable (E) very loud

10.


2.

DAWDLE (A) hang loosely (B) waste time (C) fondle (D) splash (E) paint ANGUISH (A) torment (B) boredom (C) resentment (D) stubbornness (E) clumsiness

9.

10.

RENEGADE (A) retired soldier (B) public speaker (C) complainer (D) traitor (E) comedian INTERMITTENT (A) emphatic (B) stormy (C) hopeless (D) innermost (E) periodic

3.

ACRID (A) abnormal (B) gifted (C) insincere (D) drying (E) irritating

4.

TALISMAN (A) peddler (B) mechanic (C) charm (D) juryman (E) metal key

5.

DISPATCH (A) stir up (B) leave out (C) glorify (D) persuade (E) send away

6.

BOOTY (A) navy (B) arson (C) police (D) voyage (E) spoils

7.

DEMURE (A) unforgiving (B) out-of-date (C) modest (D) uncooperative (E) overemotional

8.

CRUX (A) great disappointment (B) supporting argument (C) debatable issue (D) critical point (E) criminal act

9.

AGGRANDIZE (A) enlarge (B) condense (C) astonish (D) interpret (E) attack

10.

SUMPTUOUS (A) dictatorial (B) topmost (C) radiant (D) luxurious (E) additional

Vocabulary Test 84

3.

IMPARTIAL (A) unlawful (B) incomplete (C) unprejudiced (D) unfaithful (E) unimportant

1.

INTERLOPER (A) thief (B) intruder (C) translator (D) inquirer (E) representative

4.

FORESTALL (A) press (B) preserve (C) prevent (D) boil (E) restore

2.

SCATHING (A) bitterly severe (B) hastily spoken (C) unnecessary (D) ill-advised (E) easily misunderstood

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2.

3.

VERSATILE (A) lonesome (B) backward (C) talkative (D) brave (E) all-around FORTHRIGHT (A) frank (B) joyful (C) imaginary (D) conscious (E) preferred TUSSLE (A) meet (B) struggle (C) confuse (D) murmur (E) practice

4.

CLARITY (A) loudness (B) certainty (C) clearness (D) glamour (E) tenderness

5.

ASSESSMENT (A) appraisal (B) revision (C) property (D) illness (E) warning

6.

9.

10.

CONSTRAINTS (A) group processes (B) new laws (C) doctrines (D) current news (E) limits

7.

LOT (A) name (B) right (C) folly (D) fate (E) oath

ORTHODOX (A) accepted (B) flawless (C) contradictory (D) dignified (E) extraordinary

8.

APPREHENSION (A) gratitude (B) requirement (C) apology (D) dread (E) punishment

9.

AMENABLE (A) religious (B) masculine (C) proud (D) brave (E) agreeable


2.

COUNTERPART (A) hindrance (B) peace offering (C) password (D) balance of power (E) duplicate LOW-KEY (A) official (B) secret (C) restrained (D) unheard of (E) complicated

10.

AFFLUENT (A) neutral (B) sentimental (C) wealthy (D) handsome (E) evil

Vocabulary Test 87

3.

STIPULATION (A) imitation (B) signal (C) excitement (D) agreement (E) decoration

1.

VELOCITY (A) willingness (B) swiftness (C) truthfulness (D) smoothness (E) skillfulness

CLIQUE (A) social outcast (B) ringing sound (C) headdress (D) exclusive group (E) tangled web

4.

ANTITHESIS (A) fixed dislike (B) musical response (C) lack of feeling (D) direct opposite (E) prior knowledge

2.

ENVOY (A) messenger (B) assistant (C) planner (D) expert (E) leader

7.

NEGATE (A) polish to a bright shine (B) find quickly (C) make ineffective (D) file a protest (E) take into consideration

5.

TRANSITORY (A) short-lived (B) delayed (C) idle (D) unexpected (E) clear

3.

AUXILIARY (A) reliable (B) mechanical (C) sociable (D) supporting (E) protective

8.

IMPEL (A) accuse (B) force (C) encourage (D) prevent (E) pierce

6.

ENTRENCHED (A) filled up (B) bordered by (C) followed by (D) kept down (E) dug in

4.

PINNACLE (A) topmost point (B) feather (C) fastener (D) card game (E) small boat

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5.

6.

7.

8.

9.

10.

BOORISH (A) shy (B) rude (C) thieving (D) cunning (E) foreign ENCOMPASS (A) include (B) measure (C) attempt (D) direct (E) border on LURCH (A) trap (B) brake (C) stagger (D) waste time (E) laugh noisily EFFACE (A) rub out (B) paint red (C) build upon (D) stay in front (E) bring about ABOUND (A) do good (B) store up (C) run away (D) stand firm (E) be plentiful THWART (A) avoid (B) accuse (C) suffer (D) block (E) serve

3.

4.

5.

6.

7.

IMPROVISE (A) object loudly (B) predict (C) refuse support (D) prepare offhand (E) translate CONNIVE (A) cooperate secretly (B) enter quickly (C) pause slightly (D) push unexpectedly (E) need greatly GAIT (A) turning over and over (B) passing in review (C) manner of walking (D) fundamental attitude (E) crowd of spectators BOTCH (A) weep (B) rebel (C) resent (D) blunder (E) complain DEVOID OF (A) accompanied by (B) in the care of (C) without (D) behind (E) despite

8.

PANG (A) feeling of indifference (B) sense of duty (C) fatal disease (D) universal remedy (E) spasm of pain

9.

TEDIUM (A) bad temper (B) boredom (C) warmth (D) abundance (E) musical form

10.

INTIMATE (A) hospitable (B) well-behaved (C) familiar (D) plainly seen (E) forgiving


DELVE (A) hope for (B) believe in (C) set upon (D) take into account (E) dig into

2.

SHROUDED (A) found (B) torn (C) stoned (D) wrapped (E) rewarded

3.

EXPLOIT (A) annoy (B) join (C) use (D) mix up (E) set free

4.

RUT (A) fixed practice (B) honest labor (C) useless regret (D) happy home (E) vain hope

5.

CONSTITUENTS (A) tradesmen (B) students (C) voters (D) judges (E) ministers

6.

REPREHENSIBLE (A) distracting (B) blameworthy (C) glowing (D) frightening (E) truthful

7.

HAZARD (A) confuse (B) avoid (C) resign (D) chance (E) overlook

8.

ROBUST (A) bragging (B) huge (C) sincere (D) upright (E) sturdy


PRUNE (A) cut off (B) expect (C) put away (D) lay waste (E) remind

2.

AMIABLE (A) active (B) good-natured (C) religious (D) changeable (E) absentminded

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PIECEMEAL (A) on the spur of the moment (B) bit by bit (C) over and over (D) as a matter of course (E) from first to last

7.

MUDDLE (A) saucy remark (B) confused mess (C) delaying tactics (D) simple truth (E) great outcry

5.

DANK (A) moist (B) unhealthy (C) smoky (D) frozen (E) cloudy

INSCRUTABLE (A) disorderly (B) shallow (C) unwritten (D) painful (E) mysterious

8.

ADULTERATE (A) grow up (B) push ahead (C) make impure (D) send away (E) die off

6.

EXPRESSLY (A) definitely (B) regularly (C) quickly (D) safely (E) loudly

Vocabulary Test 90

9.

CONCEDE (A) gain (B) join (C) force (D) struggle (E) admit

7.

DISCOUNT (A) discover (B) disgrace (C) disregard (D) dislike (E) display

PLIGHT (A) final decision (B) spy system (C) plant disease (D) bad situation (E) listening post

8.

TOKEN (A) timely (B) minimal (C) stiff (D) imaginary (E) enforced

9.

DECADENCE (A) false reasoning (B) hasty retreat (C) self-assurance (D) period of decline (E) fraud

9.

10.

1.

2.

NEEDLE (A) join (B) prod (C) discuss (D) give (E) command TENTATIVE (A) forgotten (B) fabricated (C) sunny (D) temporary (E) absentee

10.

Vocabulary Test 91

HUMDRUM (A) false (B) ugly (C) uninteresting (D) mournful (E) disappointing

1.

RATIFY (A) create (B) revive (C) deny (D) confirm (E) displease

2.

5.

HORDE (A) crowd (B) framework (C) nonbeliever (D) choir (E) warrior

3.

STANCE (A) performance (B) defense (C) length (D) posture (E) concentration

1.

CLAMOR (A) magic spell (B) loose garment (C) poisoned arrow (D) loud noise (E) deep-sea fisherman

6.

RELENTLESS (A) unwise (B) fearless (C) straightforward (D) unappetizing (E) unyielding

4.

EXACT (A) fall (B) appeal (C) strain (D) loosen (E) demand

2.

CONVENTIONAL (A) inexperienced (B) close (C) foolish (D) kindly (E) usual

3.

4.

BURLY (A) useless (B) wild (C) strong (D) easy (E) medical DEBASE (A) call to mind (B) send from home (C) rely upon (D) take part in (E) reduce the value of

10.

ALACRITY (A) eagerness (B) joy (C) criticism (D) milkiness (E) fullness

Vocabulary Test 92

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3.

4.

5.

6.

7.

8.

9.

10.

INDISPUTABLE (A) unjust (B) undeniable (C) indelicate (D) indescribable (E) unconcerned PUNY (A) weak (B) humorous (C) quarrelsome (D) studious (E) innocent FACILITATE (A) make angry (B) copy (C) make easier (D) joke about (E) decorate REPULSE (A) force (B) disown (C) restore (D) repel (E) indicate CHARISMA (A) happy feeling (B) quality of leadership (C) Greek letter (D) deep hole (E) contrary view RIGOR (A) padding (B) mold (C) liner (D) building (E) strictness NOXIOUS (A) harmful (B) lively (C) uncertain (D) unprepared (E) calming ENLIGHTEN (A) please (B) put away (C) instruct (D) reduce (E) criticize


INTANGIBLE (A) incomplete (B) individual (C) vagile (D) uninjured (E) careless

2.

COMPLIANT (A) yielding (B) standing (C) admiring (D) trusting (E) grabbing

3.

ERADICATE (A) exclaim (B) heat up (C) break out (D) plant (E) eliminate

4.

ABYSS (A) great ignorance (B) evil man (C) bottomless pit (D) wide sea (E) religious sign

5.

CRITERION (A) standard (B) award (C) achievement (D) objection (E) claim

6.

9.

ASSIMILATE (A) pretend (B) absorb (C) poke (D) copy (E) expect

10. EXHORT

(A) (B) (C) (D) (E)

annoy deduct enlarge quickly urge strongly stick out


JEST (A) spout (B) trot (C) joke (D) judge (E) leap

2.

MOLEST (A) disturb (B) reduce (C) submit (D) delight (E) urge

3.

TURMOIL (A) conclusion (B) reversal (C) meanness (D) confusion (E) mistake

IRREVERENT (A) illogical (B) unimportant (C) violent (D) disrespectful (E) unafraid

4.

ORDINANCE (A) trial (B) law (C) right (D) fault (E) property

7.

SALLOW (A) temporary (B) animal-like (C) stupid (D) clean (E) yellowish

5.

LATERAL (A) financial (B) lingering (C) of the past (D) from the beginning (E) to the side

8.

RENOUNCE (A) proclaim (B) approve (C) give up (D) guarantee (E) speak plainly

6. PIGMENT

(A) (B) (C) (D) (E)

light pillar dye weed book

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VOCABULARY BUILDING THAT IS GUARANTEED TO RAISE YOUR SAT SCORE • 455 7. CONCEPT

(A) (B) (C) (D) (E)

desire thought solution method experiment

8. ORNATE

(A) (B) (C) (D) (E)

elaborate original systematic unbecoming obsolete

9. BEGRUDGE

(A) (B) (C) (D) (E)

roar mightily walk swiftly give reluctantly await eagerly seek desperately

5. RUSTLE

(A) (B) (C) (D) (E)

steal instruct strive bend tax

6. HAPLESS

(A) (B) (C) (D) (E)

optimistic uncounted unfortunate simple unyielding

7. UNPRETENTIOUS

(A) (B) (C) (D) (E)

loyal virtuous modest fair extravagant

10. REPOSE

8. BUOY

(A) (B) (C) (D) (E)

(A) (B) (C) (D) (E)

task calm strain fact surprise

Vocabulary Test 95 1. BOLSTER

(A) (B) (C) (D) (E)

reinforce thicken uncover quote bother

2. INFRINGEMENT

(A) (B) (C) (D) (E)

old age added benefit protection violation fireproofing

3. AGILE

(A) (B) (C) (D) (E)

colored healthy dull false nimble

4. DIVERSIFY

(A) (B) (C) (D) (E)

fix vary correct relieve explain

wet dry up rescue sustain direct

9. PARAGON

(A) (B) (C) (D) (E)

weak pun even distribution geometric figure moralistic story model of excellence

10. INDIGENOUS

(A) (B) (C) (D) (E)

confused native poor unconcerned wrathful

Vocabulary Test 96 1. PROLOGUE

(A) (B) (C) (D) (E)

stairway introduction conversation reading extension

2. ACKNOWLEDGE

(A) (B) (C) (D) (E)

propose strangle convict advance admit

3. INDICTMENT

(A) (B) (C) (D) (E)

accusation publisher announcer conviction trial

4. LACKLUSTER

(A) (B) (C) (D) (E)

sparkling tender misty uninspired disobedient

5. CONDOMINIUM

(A) new type of metal (B) noisy celebration (C) individually owned apartment (D) important decision (E) group meeting 6. INCUMBENT

(A) (B) (C) (D) (E)

office holder lawyer politician green vegetable sacred honor

7. POLARIZATION

(A) (B) (C) (D) (E)

performance in cold weather point of view change in opinion division into opposites cultural bias

8. GENESIS

(A) (B) (C) (D) (E)

wisdom origin classification humor night

9. DIMINUTION

(A) (B) (C) (D) (E)

devotion difference difficulty decision decrease

10. WARY

(A) (B) (C) (D) (E)

sorrowful lazy unfriendly cautious hopeful

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Vocabulary Test 97 1. SLEEK

(A) (B) (C) (D) (E)

smooth moldy loose small delicate

2. SUCCULENT

(A) (B) (C) (D) (E)

literal tardy yielding sportsmanlike juicy

3. LACERATED

(A) (B) (C) (D) (E)

bright gaunt punishable torn tied

4. SUBSIDE

(A) (B) (C) (D) (E)

pay in full become quiet return soon rush around send forth

5. ACQUITTAL

(A) (B) (C) (D) (E)

setting free agreeing with holding forth getting up steam appealing to higher authority

6. APPREHEND

(A) (B) (C) (D) (E)

inform resound frighten squeeze seize

7. IMPERATIVE

(A) (B) (C) (D) (E)

unbiased obscure repetitious compulsory unworthy

8. SUBSTANTIATE

(A) (B) (C) (D) (E)

verify replace influence condemn accept

9. RANCID

(A) (B) (C) (D) (E)

illegal rotten ashen flimsy mean

10. OUST

(A) (B) (C) (D) (E)

nag evict excel defy emerge

Vocabulary Test 98 1. TOPPLE

(A) (B) (C) (D) (E)

drink choose stray stumble overturn

2. PREVAIL

(A) (B) (C) (D) (E)

preview question relax triumph restore

3. CREDENCE

(A) (B) (C) (D) (E)

cowardice size belief variety nobility

4. DIVULGE

(A) (B) (C) (D) (E)

send shrink despair separate reveal

5. MISGIVINGS

(A) (B) (C) (D) (E)

cheap gifts feelings of doubt added treats false promises slips of the tongue

6. ACCLAIM

(A) (B) (C) (D) (E)

find restore praise judge demand

7. HALLOWED

(A) (B) (C) (D) (E)

sacred noisy deep permitted costumed

8. GUISE

(A) (B) (C) (D) (E)

ability direction guilt appearance mistake

9. TUMULT

(A) (B) (C) (D) (E)

vacation reversal swelling suffering commotion

10. REMINISCENT

(A) (B) (C) (D) (E)

amazed by obligated to suggestive of under the control of careless with

Vocabulary Test 99 1. REMIT

(A) (B) (C) (D) (E)

promise injure send profit menace

2. PANDEMONIUM

(A) (B) (C) (D) (E)

wild uproar diseased state contempt luxury gloom

3. EJECT

(A) (B) (C) (D) (E)

expose exceed extend expel excite

4. TALLY

(A) (B) (C) (D) (E)

load record hunt play move

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VOCABULARY BUILDING THAT IS GUARANTEED TO RAISE YOUR SAT SCORE • 457 5. DEVASTATE

(A) (B) (C) (D) (E)

cough ruin chop point swell

6. MAUL

(A) (B) (C) (D) (E)

trap cuddle carve throw beat

7. ANIMATION

(A) (B) (C) (D) (E)

liveliness automation carelessness dispute exchange

8. SMOLDER

(A) (B) (C) (D) (E)

show suppressed anger grow up quickly find easily report back become weary

9. PROTRUDE

(A) (B) (C) (D) (E)

make a fool of fall into put down thrust out steer clear of

10. BENEVOLENT

(A) (B) (C) (D) (E)

profitable sociable wealthy receptive charitable

Vocabulary Test 100

6. MALEFACTOR

(A) (B) (C) (D) (E)

1. UNOBTRUSIVE

(A) (B) (C) (D) (E)

annoying unquestionable inconspicuous united healthy

7. MARTIAL

(A) (B) (C) (D) (E)

2. SCRUTINY

(A) (B) (C) (D) (E)

signal plot delay investigation announcement

evil permanent unreasonable open timid

4. GARRULOUS

(A) (B) (C) (D) (E)

confused eager panting talkative informal

5. CONVERSE

(A) (B) (C) (D) (E)

junction poetry ancestor follower opposite

heavenly keen warlike tremendous masculine

8. RETORT

(A) (B) (C) (D) (E)

3. HEINOUS

(A) (B) (C) (D) (E)

fugitive joker showoff evildoer daydreamer

9.

answer jot retire recall decay

VIGILANCE (A) lawlessness (B) funeral (C) watchfulness (D) processional (E) strength

10. LESION

(A) (B) (C) (D) (E)

dream group justice style injury

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Answers to Vocabulary Tests Test 1

Test 5

Test 9

Test 13

Test 17

Test 21

Test 25

Test 29

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

D B D A E B E A E C

C B D D C E A A E C

E C E C D C A D D D

B E B B C C E A D C

A B D E E B D A B D

C E D C B D E D A D

A D E C A B E B C D

B A D E C E B E E C

Test 2

Test 6

Test 10

Test 14

Test 18

Test 22

Test 26

Test 30

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

B A E D A E C A B E

C E D C B E B E C D

B E D C B B E B A B

C E C E A E D D E E

E C B C C A E A D A

B D A E E E D A E D

E C A C B E D E D B

E C A B D E D B C A

Test 3

Test 7

Test 11

Test 15

Test 19

Test 23

Test 27

Test 31

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

C D B C B B D C A E

E A D D B B B E A B

A D A E A B A E C E

B C A C B E C D A B

B E C D A A D B A B

C D B D D D A B E D

A D C B C B B A A E

B A D A C E D E B A

Test 4

Test 8

Test 12

Test 16

Test 20

Test 24

Test 28

Test 32

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

E D E A E A A D E C

D A D E A C A C A D

C D B D B C E B D E

D C D B B A D B A A

A B D B B A C A A E

B B A E E E C E B B

E B C A B D A E A D

E A B D B A C B B E

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Test 33

Test 37

Test 41

Test 45

Test 49

Test 53

Test 57

Test 61

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

C D B C D E B B A E

C B A C E A D A E E

A D E D C A E B E D

E A D C E B B E D A

B E A C C D D A E C

E E D E B D B D D E

E C B A B A C C D A

B D B D A B D C D B

Test 34

Test 38

Test 42

Test 46

Test 50

Test 54

Test 58

Test 62

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

A B E A B D D B B C

D E E A E D C B C A

B E B B B E C D A C

B D C D B E D B A E

A C A C D B B A A B

C D E C C C B E E C

B A E D C D C E D A

D A A D A A D E D B

Test 35

Test 39

Test 43

Test 47

Test 51

Test 55

Test 59

Test 63

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

A E B A C D E D B B

E A D C B B A E C D

A B D C E C E D C A

C C D D A A B E C E

D D C B A D B B B A

C B D A C E D E A C

D D D E E B A E E B

B D C E A A D E C B

Test 36

Test 40

Test 44

Test 48

Test 52

Test 56

Test 60

Test 64

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

C B C D A D D E A E

A E C B A C D D A D

A A D D B D C A E D

B C E B E A D D B E

B E A B C C B E A A

A A D D A D B B B C

A B C E B B E D C C

B B C E E B C C A D

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Test 65

Test 69

Test 73

Test 77

Test 81

Test 85

Test 89

Test 93

Test 97

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

E A E B D D A E A E

A D E B B E B D A D

D E B E D C E E C D

E B B E D C A B D E

C A D E C E B C E A

E A B C A D C B E A

E D C A C B D E B E

C A E C A D E C B D

A E D B A E D A B B

Test 66

Test 70

Test 74

Test 78

Test 82

Test 86

Test 90

Test 94

Test 98

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

C B B D B C E D E A

D B C A B C B E D E

A C E D B B C C D A

B D C A B E D C A B

D A E C A B E E D E

E C D D A E D D E C

B D C D A E B C E D

C A D B E C B A C B

E D C E B C A D E C

Test 67

Test 71

Test 75

Test 79

Test 83

Test 87

Test 91

Test 95

Test 99

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

B B D A B E C A A C

C E B C D A B D A E

B D B C E A A D E C

C B C D B A C C D D

B A C C A B E E D E

B A D A B A C A E D

C E D E A A C B D A

A D E B A C C D E B

C A D B B E A A D E

Test 68

Test 72

Test 76

Test 80

Test 84

Test 88

Test 92

Test 96

Test 100

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

E B A B B E D C E C

A C A E D C B D B E

B C D A C E D A E B

A D A A C E A E C D

B A E C E E C D A D

A B D A C D C E B C

D E B A C D B E A C

B E A D C A D B E D

C D A D E D C A C E

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PA R T 8

GRAMMAR AND USAGE REFRESHER

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462 • GRAMMAR AND USAGE REFRESHER

The following pages will be very helpful in your preparation for the Writing ability parts of the SAT. You will find in these pages a brief but to-the-point review for just about every type of Writing Ability question that appears on the actual SAT. These are the areas covered in this study section: The Parts of Speech

Verbals

Clauses and Phrases

Mood and Voice

The Sentence and Its Parts

Adjective Modifiers

Verbs

Adverbial Modifiers

Nouns and Pronouns

Connectives

Subject-Verb Relationship

Correct Usage: Choosing the Right Word

Tense

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GRAMMAR AND USAGE REFRESHER • 463

Grammar and Usage Refresher* Chapter 1: The Parts of Speech

1a

Noun

A noun is a word that names a person, place, thing, or idea. Persons

Places

Things

Ideas

nurse Henry uncle Chicano

forest Miami house airport

banana shoe television notebook

love democracy hunger cooperation

A noun that is made up of more than one word is called a compound noun. Persons

Places

Things

Ideas

Martin Luther King cab driver movie star federal judge

high school Puerto Rico dining room Middle East

telephone book car key park bench pork chop

energy crisis arms race light year market value

1b Pronoun A pronoun is a word used in place of a noun. Buy a newspaper and bring it home. (The pronoun “it” stands for the noun “newspaper.”) Marlene went to the party, but she didn’t stay long. (The pronoun “she” stands for the noun “Marlene.”) A pronoun may be used in place of a noun or a group of nouns. Pedro wanted to see the polar bears, camels, and tropical birds, which were at the zoo. (The pronoun “which” stands for the nouns “polar bears, camels, and tropical birds.”) When Mark, Steven, Teresa, and Barbara became eighteen, they registered to vote. (The pronoun “they” stands for the nouns “Mark, Steven, Teresa, and Barbara.”) The noun that the pronoun replaces is called the antecedent of the pronoun. The plates broke when they fell. (The noun “plates” is the antecedent of the pronoun “they.”) Avoid confusion by repeating the noun instead of using a pronoun if more than one noun might be considered to be the antecedent. The lamp hit the table when the lamp was knocked over. (Not: The lamp hit the table when it was knocked over.) *An index to this entire Grammar Refresher section begins on page 519.

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1c

Verb A verb is a word or group of words that expresses action or being. The plane crashed in Chicago. (action) Soccer is a popular sport. (being)

1d Adjective An adjective is a word that modifies a noun or pronoun. Note: In grammar, to modify a noun means to describe, talk about, explain, limit, specify, or change the character of a noun. Susan brought us red flowers. (The adjective “red” describes the noun “flowers.”) Everyone at the party looked beautiful. (The adjective “beautiful” describes the pronoun “everyone.”) Several people watched the parade. (The adjective “several” does not actually describe the noun “people”; it limits or talks about how many “people” watched the parade.) Those shoes are her favorite ones. (The adjective “favorite” defines or specifies which “ones.”) They have two children. (The adjective “two” limits or specifies how many “children.”) 1e

Adverb An adverb is a word that modifies the meaning of a verb, an adjective, or another adverb. The librarian spoke softly. (The adverb “softly” describes or explains how the librarian “spoke.”) Jackie Onassis was extremely rich. (The adverb “extremely” talks about or specifies how “rich” Jackie Onassis was.) The job is ver y nearly completed. (The adverb “very” limits or specifies how “nearly” the job is completed.)

1f

Preposition A preposition is a word that connects a noun or pronoun to another word in the sentence. The mayor campaigned throughout the city. (The preposition “throughout” connects the noun “city” to the verb “campaigned.”) A preposition connects a noun or pronoun to another word in the sentence to show a relationship. The wife of the oil executive was kidnapped. A friend of mine is a good lawyer. The strainer for the sink is broken. The floor under the sink is wet. David wants to work in the city. The accident occurred about eight o’clock.

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1g

Conjunction A conjunction is a word that joins words, phrases, or clauses. Alan’s father and mother are divorced. (two words joined) phrase

phrase

Is your favorite song at the end or in the middle of the record? (two phrases joined) You may swim in the pool, but don’t stay long. (two clauses joined) (See Chapter 12 for a discussion of how prepositions and conjunctions act as connectives.) 1h Interjection An interjection is a word (or group of words) that expresses surprise, anger, pleasure, or some other emotion. Aha! I’ve caught you. Oh no! What have you done now? An interjection has no grammatical relation to another word. Ouch! I’ve hurt myself. 1i

A word may belong to more than one part of speech, depending on its meaning. Example 1 Everyone but Sam was invited to the wedding. (preposition) The Orioles won the pennant, but the Angels came close to winning. (conjunction) Harry has but ten dollars left in his bank account. (adverb) Example 2 He lives up the street. (preposition) It’s time to get up. (adverb) The sun is up. (adjective) Every life has its ups and downs. (noun) I’ll up you five dollars. (verb) Note: Just for fun—what is the part of speech of the word “behind” in this sentence? Attempting to save Annie, the fireman ran for the door, dragging her behind. Our answer is an adverb, meaning “at the rear.” If your answer was a noun—Oh my! The noun means a certain part of the human body. We won’t tell you which part.

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Chapter 2: Clauses and Phrases

2a

Clauses A clause is a group of words within a sentence. From his room, he could see the park. (one clause) The children loved the man who sold ice cream. (two clauses) A clause contains a subject and a verb. subject

verb

Before the race, the jockeys inspected their horses. (one clause) subject

verb

subject

verb

When the rain stopped, the air was cooler. (two clauses) 2b There are two types of clauses: main and subordinate.* main clause

During the riot, several people got hurt. subordinate clause

main clause

When she won the lottery, Mrs. Ya-ching shouted with joy. A main clause makes sense by itself. We got the day off. A main clause expresses a complete thought. The fire was put out. (Not: When the fire was put out.) It rained this morning. (Not: Because it rained this morning.) A subordinate clause does not make sense by itself. While the washing machine was broken, we couldn’t wash anything. (The subordinate clause does not make sense without the rest of the sentence.) Because a subordinate clause does not make sense by itself, a subordinate clause cannot stand as a complete sentence. While the washing machine was broken . . .

*A main clause may be called an independent clause. A subordinate clause may be called a dependent clause.

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A subordinate clause depends on a par ticular word in a main clause to make the subordinate clause mean something. main clause

subordinate clause

Jack abandoned the car that had two flat tires. (The subordinate clause depends on the noun “car” in the main clause to describe the car.) main clause

subordinate clause

The job was offered to Ann because she was best qualified. (The subordinate clause depends on the verb “was offered” in the main clause to explain why the job was offered.) main clause

subordinate clause

My new neighbor is the one who is waving. (The subordinate clause depends on the pronoun “one” in the main clause to tell who is waving.) A subordinate clause may be used in a sentence as an adjective, an adverb, or a noun. Woody Allen’s new film is the funniest movie that he has made yet. (The subordinate clause acts like an adjective because it modifies—talks about—the noun “movie.”) The child giggled while he was asleep. (The subordinate clause functions like an adverb because it modifies the verb “giggled.”) Please tell me what this is all about. (The subordinate clause acts like a noun because it is the object of the action verb “tell.”) 2c

Phrases A phrase is a group of words within a sentence. Thurmon Munson died in a plane crash. (one phrase) Let’s sit under that apple tree. (one phrase) At the top of the hill

there were some cows grazing. (two phrases)

The phrase itself does not contain a subject or a verb. subject

verb

Many streets in the city need repairs. A phrase does not make sense by itself. Ellen has a collection of beautiful earrings. (The phrase “of beautiful earrings” does not make sense by itself; therefore, the phrase cannot stand alone as a complete sentence.) A phrase may begin with a preposition, a participle, a gerund, or an infinitive. preposition

Put the milk into the refrigerator. (prepositional phrase)

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468 • GRAMMAR AND USAGE REFRESHER participle

There are several people waiting in line. (participial phrase) gerund

Running ten miles a day is hard work. (gerund phrase) infinitive

To sing well takes a lot of practice. (infinitive phrase) A phrase may be used as

a noun, an adjective, or an adverb.

A doctor’s job is to heal people. (The infinitive phrase acts like a noun because it names the doctor’s job.) Raising his hands, the pope blessed the crowd. (The participial phrase acts like an adjective because it describes the pope.) Most stores close at five o’clock. (The prepositional phrase acts like an adverb because it tells when most stores close.)

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Chapter 3: The Sentence and Its Parts

3a

A sentence is a group of words that has a subject and a verb. subject

verb

The concert began at midnight. subject

verb

During the storm, the electricity was knocked out. 3b

A sentence may be declarative, interrogative, or exclamator y. A declarative sentence states or asserts. Inflation is a serious problem. An interrogative sentence asks a question. How long must we suffer? An exclamator y sentence expresses emotion* What a fool he is! A sentence expresses a complete thought. The price of gold has gone up. Bus ser vice will resume on Friday morning. Note: Because a sentence expresses a complete thought, a sentence makes sense by itself. Peter likes to tend his vegetable garden. (complete thought) Peter likes. (incomplete thought—not a sentence) The gasoline shortage created serious problems. (complete thought) The gasoline shortage. (incomplete thought—not a sentence).

3c

The four types of sentences according to structure are the following: (1) Simple

Everyone likes music.

(2) Compound

The Simons put their house up for sale on Friday, and it was sold by Monday.

(3) Complex

If you want good Szechuan cooking, you should go to the Hot Wok Restaurant.

(4) Compound-Complex

Bob met Sally, who was in town for a few days, and they went to a museum.

*An “exclamatory sentence” is sometimes called an “imperative sentence.”

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3d Simple sentence A simple sentence is made up of one main clause only. I love you. A simple sentence may be of any length. The old man sitting on the park bench is the father of a dozen men and women besides being the grandfather of nearly forty children. Note: A simple sentence does not have a subordinate clause in it. 3e

Compound sentence A compound sentence has two or more main clauses. main clause

conjunction

Conrad and Isabel got married,

and

main clause

they invited several friends to a party. main clause

conjunction

main clause

Stuart attended college, but he left after a year. Each main clause in a compound sentence may stand by itself as a simple sentence—as long as the conjunction is left out. conjunction

Carlos will arrive by plane tonight, and Maria will go to the airport to meet him. (compound sentence) Carlos will arrive by plane tonight. (simple sentence) Maria will go to the airport to meet him. (simple sentence) Note: A compound sentence does not have any subordinate clauses. 3f

Complex sentence A complex sentence contains only one main clause and one or more subordinate clauses. subordinate clause

main clause

After he signed the treaty, President Bush asked the Senate to ratify it. (one main clause and one subordinate clause) subordinate clause

main clause

Although they are expensive to install, solar heating systems save money and energy, subordinate clause

which are hard to get these days. (one main clause and two subordinate clauses) subordinate clause

Because he came from the planet Krypton,

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GRAMMAR AND USAGE REFRESHER • 471 main clause

subordinate clause

Superman had special powers that no one on Earth could equal, subordinate clause

though many people have tried. (one main clause and three subordinate clauses) 3g

Compound-complex sentence A compound-complex sentence is made up of two or more main clauses and one or more subordinate clauses. subordinate clause

After his store burned down, main clause

Mr. Crossman rented the store across the street, main clause

and his business continued to do well. (two main clauses and one subordinate clause) main clause

Eric wanted to go to the new disco, subordinate clause

which he had heard was a great place, main clause

but he did not want to see his ex-wife, subordinate clause

who worked there. (two main clauses and two subordinate clauses) 3h The parts of a sentence The basic parts of a sentence are a subject, a verb, and a complement.* subject

verb

complement

The waiter brought the soup. compound subject

verb

complement

Mason and Lucy sold me their stereo.

*The complement is discussed on pages 477–478.

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3i

Subject A subject of a sentence is the word (or group of words) that tells who or what is being talked about. Ann Landers gives advice to millions of Americans. (Because Ann Landers is being talked about, “Ann Landers” is the subject of the sentence.) High taxes caused many businesses to close. (Because we are told that high taxes caused businesses to close, the noun “taxes” is the subject of the sentence.) Whoever goes to bed last should shut off the lights. (Because we are told that whoever goes to bed last should do something, the noun clause “whoever goes to bed last” is the subject of the sentence.) Brushing one’s teeth and getting checkups regularly are two important parts of good dental care. (Because brushing one’s teeth and getting checkups are discussed, the two gerund phrases are the compound subject of the sentence.)

3j

A subject may be a noun, pronoun, verbal, phrase, or clause. (1) A subject is usually a noun. Our wedding will be held outdoors. The White House is the home of the president. The police arrested the anti-nuclear energy demonstrators. (2) A subject may be a pronoun. He always gets his way. (personal pronoun used as the subject) Hers is the tan raincoat. (possessive pronoun used as the subject) What did you do? (interrogative pronoun used as the subject) That is my car. (demonstrative pronoun used as the subject) Ever yone was happy. (indefinite pronoun used as the subject) (3) A subject may be a verbal.* To begin is the hardest part of the job. (infinitive used as the subject) Jogging is good exercise. (gerund used as a subject) Note: A participle may not be used as a subject. (4) A subject may be a phrase. Smoking cigarettes is unhealthy. (gerund phrase used as a subject) To obey the law is everyone’s duty. (infinitive phrase used as a subject) (5) A subject may be a subordinate clause. Whatever you decide is all right. That Danny had cancer saddened his friends. What will happen is going to surprise you. Who will star in the movie will be announced.

*See Chapter 8.

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3k

Verb A verb is a word or group of words that usually tells what the subject does. Annie skated down the street. Your baby has dropped his toy. President Nixon resigned. The telephone is ringing. Two or more verbs may have one subject. They defeated the Cubs but lost to the Pirates. Dick works during the day and goes to school at night. A verb may express a state or condition. Lynn appears puzzled. (Or: Lynn appears to be puzzled.) The stew tastes delicious. Jason and Martha are good friends.

3l

The three kinds of verbs are transitive, intransitive, and linking.

3m A transitive verb tells what its subject does to someone or to something. The cat caught the mouse. Phil washed the dishes. Carol’s mother slapped the boy. 3n An intransitive verb tells what its subject does. The action of the intransitive verb does not af fect someone or something else. The old man slept in his chair. The audience applauded. All of the job applicants waited patiently. Note: Many verbs may be transitive or intransitive. He will return the book tomorrow. (transitive) The manager will return in an hour. (intransitive) Whether a verb is transitive or intransitive depends on how it is used in the sentence. Chuck opened the package. (The verb is transitive because the action was carried out on something.) The door opened slowly. (The verb is intransitive because the action by the subject “door” did not affect anything else.) 3o

A linking verb links the subject with a noun or a pronoun or an adjective. “Jaws” was a terrifying film. (noun) It’s I.* (pronoun)

*In spoken English, it is acceptable to say “It’s me” or “It’s us.” It is not acceptable, however, to say “It’s him,” “It’s her,” or “It’s them.”

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The child in this old photograph is I. (pronoun) The girl who loves Peter is she. (pronoun) The Beatles were popular in the 1960’s. (adjective) A linking verb may link the subject with an infinitive, a gerund, or a noun clause. Stephanie’s greatest pleasure is to sing. (infinitive) Herb’s mistake was lying. (gerund) David’s new job seemed what he had hoped for. (noun clause) Linking verbs are to be, to appear, to grow, to seem, to remain, to become, and verbs that involve the senses, such as to look, to smell, to feel, to sound, and to taste. Karen and Valerie are sisters. Ben is strong. Eric appears healthy. The situation at the prison remains tense. Gertrude feels better. Jim sounds angry. A verb that appears to be a sense-linking verb may not actually be a sense-linking verb. The milk smells sour. (linking verb) The dog smells the fire hydrant. (transitive verb) Tony looked sad. (linking verb) Rosie looked through the window. (intransitive verb) Note: The use of a par ticular verb determines whether that verb is sense-linking or transitive or intransitive. 3p Transitive verb

Intransitive verb

Linking verb

1. Expresses action

1. Expresses action

1. Does not express action

2. Is followed by a direct object which receives the action

2. Is not followed by a direct object

2. May be followed by a noun or an adjective

subject

trans. verb

direct object

Keith shot a deer.

subject

intrans. verb

Jimmy grinned.

subject

link. verb

predicate noun

Juanita is a nurse. subject

link. verb

Lenny looks

predicate adjective

sick.

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Chapter 4: Verbs

4a

Five characteristics of ever y verb are number, person, tense, mood, and voice.

4b Number shows whether the subject of the verb is singular or plural. Maggie drives well. (singular) Adam and Peter drive dangerously. (plural) Joan’s grandmother is in Atlanta. (singular) Arthur’s parents are from Texas. (plural) A verb must always agree in number with its subject. subject

verb

Emily lives alone. (subject and verb both singular) subject

subject

verb

Dennis and Chuck live together. (subject and verb both plural) 4c

Person tells whether the subject of the verb is speaking, being spoken to, or being spoken about. I am the person in charge. (first person) You are my best friend. (second person) Bill is not here. (third person) I swim at the YMCA. (first person) You come with me. (second person) Rosa speaks Spanish and French. (third person) All three persons may be singular or plural in number. Singular

Plural

First person

I run

we run

Second person

you run

you run

Third person

he runs she runs

they run

it runs Note: The same verb form frequently is used for different persons and different numbers. I love ice cream. (first person singular) We love ice cream. (first person plural) They love ice cream. (third person plural)

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4d Tense shows when the action of the verb takes place—whether in the present, the past, or the future. A plane is passing over our house right now. (present) Our guests are here. (present) Two U.S. astronauts walked on the moon in 1969. (past) The workmen were here yesterday. (past) We’ll pay you tomorrow. (future) Many people will be at the party tomorrow. (future) 4e

Mood indicates how a sentence is used—whether it is a statement or a question, a command or a request, a wish or a condition. Dinner is ready. (statement) Does Elizabeth work in New Jersey? (question) Go away! (command) Please pass me the bread. (request) If it doesn’t rain, we can go. (condition) The three kinds of moods are indicative, imperative, and subjunctive. The indicative mood is used to express a statement or a question. Two firemen were injured in the blaze. (statement) Are you going out tonight? (question) The imperative mood expresses a command or a request. Turn off that radio! (command) May I have a menu? (request—not question) Note: The imperative mood is frequently indicated by leaving out the pronoun “you.” (You) Stop that! The subjunctive mood may be used to show that a wish rather than a fact is being expressed. I wish I were ten years younger.

4f

Voice indicates whether the subject acts or is acted upon. The dog barked at the stranger. The baby was kissed several times. A verb in the active voice shows that the subject is doing something. The thieves wounded the bank teller. (active voice) The curtains blocked our view. (active voice) A verb in the passive voice shows that something is being done to the subject. The garbage was picked up this morning. (passive voice) Tyrone’s car is being washed. (passive voice)

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4g

Complement A complement may be one or more words that come after either a transitive or a linking verb. complement

Fire destroyed the building. (transitive verb) complement

The cat seemed startled. (linking verb) complement

complement

Tony bought his wife a silver necklace. (transitive verb) complement

Adam will be president someday. (linking verb) A complement completes the meaning of the verb. The junta took control of the government. A baseball broke the window. 4h The four ways that a complement may be used in a sentence are 1) as a direct object of the verb, 2) as an indirect object of the verb, 3) as a predicate noun,* and 4) as a predicate adjective. Sally waters her garden every day. (direct object, receiving the action of the verb) Vincent gave his brother a basketball. (indirect object, telling to whom the action of the verb was directed) Note: The noun “basketball” is the direct object of the transitive verb “gave”; therefore, “basketball” is also a complement. Arthur Fiedler was the conductor of the Boston Pops. (predicate noun, renaming the subject after the linking verb) Alaska is huge. (predicate adjective, describing the subject after the linking verb) 4i

A complement used as a direct object of the verb may be a noun, a pronoun, or a subordinate clause. Uncle Nate plants vegetables each spring. (noun used as direct object) You should see her now. (pronoun used as direct object) Tell me what you know about life insurance. (subordinate clause used as direct object)

4j

A complement used as an indirect object of the verb may also be a noun, a pronoun, or a subordinate clause. The nurse sent the patient a bill. (noun used as indirect object) Will you do me a favor? (pronoun used as indirect object) Give whoever calls today this information. (subordinate clause used as indirect object) Note: From the three examples above, you can see that an indirect object must always be accompanied by a direct object.

*A predicate noun is also called a predicate nominative.

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The three sentences above—which have indirect objects—may be expressed in a different way. The nurse sent a bill to the patient. Will you do a favor for me? Give this information to whoever calls today. In these three sentences, the prepositional phrases serve the purpose of indirect objects. 4k A complement that acts as a predicate noun may be a noun, a pronoun, a verbal, a phrase, or a clause. Juan’s uncle is a bus driver. (noun) It is she. (pronoun) Fred’s favorite sport is sailing. (gerund) President Sadat’s desire is to make peace. (infinitive phrase) Fixing cars is what Tom does best. (noun clause) 4l

A complement that acts like a predicate adjective may be an adjective or an adjective phrase. Laverne and Shirley are funny. (adjective) The lecture was about alcoholism. (adjective phrase) Note: Both predicate nouns and predicate adjectives may be called predicate complements.

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Chapter 5: Nouns and Pronouns

5a

Nouns The five types of nouns are 1) proper, 2) common, 3) collective, 4) concrete, and 5) abstract.*

5b A proper noun names a par ticular person, place, or thing. Cesar Chavez, San Clemente, Statue of Liberty (Proper nouns always begin with a capital letter.) 5c

A common noun names a general sort of person, place, or thing. waitress, store, table

5d A collective noun names a group of individuals. congregation, class, political party (A collective noun is singular in form, but it refers to many people.) 5e

A concrete noun names any material object that is inanimate. apple, hat, ball, box, desk, book, shirt

5f

An abstract noun names a quality, state, or idea. truth, motion, beauty

5g

Pronouns The six kinds of pronouns are 1) personal, 2) relative, 3) interrogative, 4) indefinite, 5) demonstrative, and 6) reflexive.

5h A personal pronoun stands for the speaker, the person spoken to, or the person or thing spoken about. I am going out. (The first person “I” is speaking.) You should see the traffic jam downtown. (The second person “you” is being spoken to.) She wants to become a lawyer. (The third person “she” is being spoken about.)

*A noun may be of more than one type. For example, “table” is both a common noun and a concrete noun.

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The personal pronouns are the following: I, you, he, she, it, we, they, me, us, him, her, them The possessive forms of the personal pronouns are the following: my, mine, yours, his, hers, its, our, ours, their, theirs A pronoun should be in the same person as the noun or pronoun it refers to. The tree was damaged when lightning struck it. (noun and pronoun in third person) Ever yone knows that he should dress well to make a good impression. (both pronouns in third person) (Not: Ever yone knows that you should . . . ) 5i

The relative pronouns are the following: who (whom), which, what, that A relative pronoun may begin a subordinate clause. The child, who was alone, looked unhappy. A relative pronoun connects the main clause to the subordinate clause. The problem was in the gas line, which was rusty. (The relative pronoun “which” joins the main clause to the subordinate clause it begins.) A relative pronoun stands for a noun in the main clause. Sharon gave me the money that I needed. (The relative pronoun “that” stands for the noun “money” in the main clause.) When to use the relative pronoun “whom” “Whom” is the objective case form of “who.” We use “whom” as a direct object, an indirect object, or an object of the preposition. The men whom you see are waiting for work. (The relative pronoun “whom” is the direct object of the verb “see.”) Hansen is the person to whom Wilmot gave the bribe money. (The relative pronoun “whom” is the indirect object of the verb “gave.”) The typewriter was stolen by the messenger about whom the office manager had been suspicious. (The relative pronoun “whom” is the object of the preposition “about.”)

5j

An interrogative pronoun asks a question. Who wants to start first? What did Richard do then? Which should I take? Whose is this jacket? Whom do you want to speak to?

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5k An indefinite pronoun refers to a number of persons, places, or things in a general way. None of the dishes was broken. Mark finds ever ything about boats interesting. I’ll bring you another. Some of my friends buy lottery tickets. Other commonly used indefinite pronouns are the following: any, both, few, many, most, one, other, several, such 5l

A demonstrative pronoun points out a specific person or thing. This is not my handwriting. May I have two of those? That is my brother. These are my best friends. Note: Interrogative, indefinite, and demonstrative pronouns may be used as adjectives. Which dessert do you want? (interrogative adjective) Ever y time I try to skate I fall down. (indefinite adjective) That dress costs too much. (demonstrative adjective)

5m

A reflexive pronoun refers back to the noun it stands for. I hurt myself while jogging. Amy considers herself an adult. A reflexive pronoun may be the direct object of a verb, the indirect object of a verb, the object of a preposition, or a predicate noun. Kim pushed himself and finished the race. (direct object) Ray bought himself a new watch. (indirect object) Buffie likes to be by herself. (object of a preposition) Mr. Thompson is just not himself lately. (predicate nominative) Note: Do not use “hisself ” for “himself,” or “theirselves” for “themselves.”

5n Three characteristics shared by all nouns and pronouns are gender, number, and case. 5o

Gender indicates the sex of the person or thing named—whether masculine, feminine, or neuter. Adam wants some ice cream, but he is on a diet. (“Adam” and the pronoun “he” are both masculine in gender.) Alice said she was ready. (“Alice” and the pronoun “she” are both feminine in gender.) The movie was good, but it was too long. (“Movie” and the pronoun “it” are neither masculine nor feminine; therefore, they are both neuter in gender.) A pronoun should be in the same gender as the noun it refers to.

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5p Number indicates whether one or more than one person or thing is named. Here is a letter for you. (The one letter is singular in number.) Many cars were involved in the accident. (Many “cars” are plural in number.) Note: A collective noun is singular in form but usually plural in meaning. The audience was upset by the delay. (“Audience” in singular in number, although many people are in the audience.) A pronoun should be in the same number as the noun it refers to. The dishes are not clean, so don’t use them. (“Dishes” and the pronoun “them” are both plural in number.) Hockey is a lot of fun, but it is rough. (“Hockey” and the pronoun “it” are both singular in number.) A pronoun that refers to a collective noun that is considered as a unit should be singular in number. The home team won its final game of the season. A pronoun that refers to a collective noun that is considered as a group of individuals should be plural. The visiting team felt they deserved to win. A pronoun that refers to an indefinite pronoun antecedent must be singular. Almost anyone can earn a good living if he or she works hard. A pronoun must be singular if it refers to singular antecedents joined by “or” or “nor.” Neither Earle nor Jeff could find his coat. 5q Case shows how a noun or pronoun is used in a sentence. They stayed out all night. (“They” is the subject.) Natalie knew him. (“Him” is the object of the transitive verb.) Craig thinks this hat is his. (“His” is a pronoun that shows ownership.) The three cases are nominative, objective, and possessive. 5r

The nominative case names the subject of a verb or the predicate noun of a linking verb. Susan and I will call you tonight. (subjects) My best friends are Katherine and you. (predicate nouns) A noun in the nominative case usually is placed before a verb. Mr. Garcia opened a dry cleaning business. Ida answered the telephone.

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Personal pronouns in the nominative case have the following forms: I, you, he, she, it, we, they The subject of a subordinate clause must be in the nominative case even if the clause itself acts as a direct object or an object of a preposition. Show me who is waiting to see me. (subordinate clause as direct object) Discuss this form with whoever applies for the job. (subordinate clause as object of a preposition) 5s

The objective case indicates that nouns and pronouns act as direct objects, indirect objects, or objects of prepositions. The storm forced them to stay home. (direct object) Victor enjoyed meeting her. (direct object) Sally called us, Mar y and me, into her office. (direct objects) The cab driver gave me good directions. (indirect object) Our supervisor showed him and me some contracts. (indirect objects) Annette had trouble teaching them how to type. (indirect object) Several of us want more food. (object of the preposition) Between you and me, I don’t like our boss. (objects of the preposition) Note: Each noun or pronoun in a compound object must be in the objective case. A noun is in the objective case if it is placed after a transitive verb or after a preposition. He saw Greta Garbo. Ernie went into the store. Personal pronouns in the objective case have the following forms: me, you, him, her, it, us, them

5t

Only two personal pronouns “we” (“us”) and “you”—may also be used as adjective pronouns. We women have responded to the challenge of the 2000’s. They are discriminating against us women. You boys should play more quietly. Note: The adjective pronoun “we” is in the nominative case when it modifies a subject. The adjective pronoun “us” is in the objective case when it modifies an object of a verb or an object of a preposition. We Republicans support President Bush’s bid for re-election. (nominative case when modifying subject) Mom sent us children to bed. (objective case when modifying direct object of verb) Won’t you give us boys a chance to earn some money? (objective case when modifying indirect object of verb) Many children were on the plane with us adults. (objective case when modifying object of a preposition)

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5u The objective case is used by nouns and pronouns that are the subject of an infinitive. Paul’s father wants him to help paint the house. Should Fred ask her to join the club? A noun or pronoun following the infinitive to be must, like its subject, be in the objective case. Pat didn’t expect my friend to be him. Note: If the infinitive to be has no subject, the noun or pronoun that comes after the infinitive is in the nominative case. My twin brother is often thought to be I. (nominative case) 5v

The possessive case indicates ownership. Martha’s home is in Ohio. This book is mine. Possession is generally shown by using an apostrophe: Bumbry’s error

men’s room

child’s toy

ship’s crew

Ownership may be shown by an “of ” phrase. The handle of the door is broken. The “of ” phrase is used in formal English to show possession by inanimate things or to avoid awkward constructions. The passage of the bill now in Congress will mean lower taxes. (Not: The bill’s passage. . . . ) The sister of my uncle’s wife is eighty years old. (Not: My uncle’s wife’s sister. . . . ) Personal and relative pronouns have distinct forms to show the possessive case. The following are personal pronouns (possessive form): my, mine, your, yours, his, her, hers, our, ours, their, theirs, its* That dress is hers. Ours is the house on the left. “Whose” is a relative pronoun. (possessive form)† No one knows whose it is. The possessive forms my, your, his, our, their,‡ and whose are called adjective pronouns because they modify nouns. Your shirt has a button missing. My family is very large.

*“Its” is the possessive form of the personal pronoun “it.” “It’s” is a contraction of “it is.” † “Whose” is the possessive form of the relative pronoun “who”; “who’s” is a contraction of “who is.” ‡ “Their” is the possessive form of the relative pronoun “they”; “they’re” is a contraction of “they are.”

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Their apartment costs a lot of money. The woman whose typewriter I borrowed, gave it to me. The possessive case is used by nouns and pronouns that come before a gerund. Bubba’s shouting attracted a large crowd. (noun) My being sick caused me to miss an important lecture. (pronoun) The possessive case of a compound noun is indicated by adding’s to the last word of the compound noun. A movie star’s life is glamorous. The Governor of California’s speech attacked the president. Pope John Paul II’s visit to the United States pleased millions. Note: The plural of a compound noun is formed by adding to the principal noun. chief of police (singular)

chief of police’s (singular possessive)

chiefs of police (plural)

chiefs of police’s (plural possessive)

5w An appositive is a noun or pronoun usually placed next to another noun or pronoun to rename it. Two guys, Nestar and his cousin, were already there. (identifies the subject) Clarinda’s dog Sonya eats only hamburgers. (renames the subject) Note: An appositive must always be in the same case as the noun it renames. We, my brother and I, are going hunting together. (both subject and appositive in nominative case) Uncle Joe gave us, Stuart and me, tickets to the World Series. (both object and appositive in case) 5x

Direct address and nominative absolute constructions are always in the nominative case. Direct address consists of a noun (or pronoun) that names a par ticular person when someone else addresses that person. Willy, please come here immediately. A nominative absolute consists of a noun plus a participle. The money having been spent, the boys decided to go home.

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Chapter 6: Subject-Verb Relationship

6a

A verb must agree with its subject in number and in person. Dr. Shu has office hours from 8 until 4. (The third person singular form of “to have” agrees with the subject “Dr. Shu.”) Robin and I play squash every Tuesday. (The first person plural form of “to play” agrees with the compound subject “Robin and I.”)

6b Collective nouns are followed by singular or plural verbs according to the sense of the sentence. The jury has asked for more time. (The third person singular is used because the jury is considered to be a unified body.) The jury are unable to agree. (The third person plural is used because the jury is considered to be a group of twelve persons.) To summarize, a collective noun is singular when it refers to a group as a single unit. A minority in Congress is delaying passage of the bill. A collective noun is plural when it refers to the individual members of the group. A minority of Congressmen want to defeat the bill. 6c

Some indefinite pronouns are always singular in meaning. Each of the candidates wants an opportunity to discuss his beliefs. Anyone is allowed to use the public beach. Any one of us is willing to help. Some indefinite pronouns are always plural in meaning. Many of the drawings were beautiful. A few of the windows were broken. Several of Joe’s friends are sorry that he left.

6d A verb should be singular if its subject has “ever y” or “many a” just before it. Many a woman feels entitled to more in life than just housework. Ever y man, woman, and child wants to be happy. Some indefinite pronouns may be singular or plural, depending on the meaning of the sentence. Some of the books have been lost. Some of the work was completed. All of the ice cream is gone.

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All of the men have left. Most of the talk was about football. Most of the people were dissatisfied. 6e

When singular subjects are joined by “or” or “nor,” the subject is considered to be singular. Neither the mother nor her daughter was ever seen again. One or the other of us has to buy the tickets.

6f

When one singular and one plural subject are joined by “or” or “nor,” the subject closer to the verb determines the number of the verb. Neither the plumber nor the painters have finished. Either the branch offices or the main office closes at 4.

6g

When the subjects joined by “or” or “nor” are of dif ferent persons, the subject nearer the verb determines the person. She or you are responsible. You or she is responsible. To avoid such awkward sentences, place a verb next to each subject. Either she is responsible or you are. Either you are responsible or she is.

6h Even if the verb comes before the subject, the verb agrees with the true subject in number and person. Are the cat and the dog fighting? (The cat and the dog are . . . ) Coming at us from the left was an ambulance. (An ambulance was . . . ) There are two things you can do.* (Two things are . . . ) There is only one bottle left.* (Only one bottle is . . . ) 6i

Interrogative pronouns and the adverbs “where,” “here,” and “there” do not af fect the number or person of the verb when they introduce a sentence. subject

What is the name of your friend? subject

What are the addresses of some good restaurants? subject

Who is the man standing over there? subject

Who are those people?

*In this sentence, there is an expletive. An expletive is a word that gets a sentence started, but it is not a subject. Another expletive is it.

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488 • GRAMMAR AND USAGE REFRESHER subject

Here comes my friend. subject

Here come my parents. 6j

When a predicate noun (following a linking verb) dif fers in number from the subject, the verb must agree with the subject. Our biggest problem is angry customers. More gas guzzlers aren’t what this country needs.

6k Parenthetical phrases or other modifiers that come between the subject and verb do not change the number or person of the true subject—which the verb agrees with. The amount shown, plus interest, is due on Friday. The president, together with his advisers, is at Camp David.

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Chapter 7: Tense

7a

Tense specifies the moment of an action or condition. We are walking to the park. (present moment) We will walk to the park tomorrow. (future moment) We walked to the park yesterday. (past moment) I have worked here for three years. (action begun in the past and continued into the present) I had worked in Chicago for four years before I left. (past action completed before another past action) I will have worked here six months next Friday. (past action to be completed sometime in the future)

7b The six tenses are present, past, future, present perfect, past perfect, and future perfect. 7c

The present tense shows that an action is happening in the present or that a condition exists now. I live here. (action) He is busy now. (condition) The present tense forms of to work, to have, and to be follow: to work I work

to have I have

to be I am

you work

you have

you are

he she works it

he she has it

he she is it

we work

we have

we are

you work

you have

you are

they work

they have

they are

The present tense may indicate habitual action or habitual condition, or a general truth. Judy leaves her office every day at 5 o’clock. (habitual action) Dana is allergic to chocolate. (habitual condition) Two and two are four. (general truth)

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The present tense may express future time with the help of an adverb. adverb

Gary flies to Washington tomorrow. adverb

We are going to see a movie tonight. 7d The present perfect tense shows that an action which began in the past is still going on in the present. Betsy and I have been in New York for two years. (and are still in New York) The Johnson family has owned a plumbing supply company for sixty years. (and still owns it) The present perfect tense may show that an action begun in the past was just completed at the present time. Our men have worked on your car until now. Charlayne has just walked in. The present perfect tense is formed with have or has and a past participle. I have eaten too much. Nina has always loved music. 7e

The past tense shows that an action occurred some time in the past but has not continued into the present. Laura’s doctor advised her to lose weight. The plane landed on time. Susan was living in Philadelphia then. (progressive form) We went along for the ride. If the verb in the main clause is in the past tense, the verb in the subordinate clause must also be in the past tense. The surgeon told his patient that an operation was necessary. (Not: The surgeon told his patient that an operation will be necessary.) Lenny said that he would meet Frank at 7:30. (Not: Lenny said that he will meet Frank at 7:30.) The past tense (first, second, and third person—singular and plural) is often formed by adding “ed” to the infinitive (without “to.”) Jim helped us many times. We called you last night.

7f

The past perfect tense indicates that an action was completed before another action began. I remembered the answer after I had handed in my exam. Kenny had bought the tickets before he met Ruth. Margaret had worked very hard, so she took a vacation. Note: The past tense shows that an event happened at any time in the past, but the past perfect tense indicates that an event happened before another event in the past.

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Paula had finished dressing before I woke up. (Not: Paula finished dressing before I woke up.) Jake had already left by the time I arrived.) (Not: Jake already left by the time I arrived.) The past perfect tense is formed with “had” and a past participle. Peter had said he would call before twelve. 7g

The future tense indicates that an action is going to take place sometime in the future. All of us will pay more for heat this winter. The weatherman says it will rain tomorrow. Will you join us for lunch, Eric? I’ll go away this weekend. The future tense is formed with “will” and the infinitive (without “to”). Don will take you to the airport.

7h The future perfect tense is used to express a future action that will be completed before another future action. By the time we get home,* my parents will have gone to bed. We’ll start eating after you (will) have washed your hands. Helena will have finished her work when we meet her at the office. The future perfect tense is formed with “will have” and a past participle. Patty will have quit her job by Christmas. 7i

All six tenses may be expressed in a progressive form by adding a present participle of a verb to the appropriate form of “to be.” The Cosmos are winning. (present progressive) The Cosmos were winning. (past progressive) The Cosmos have been winning. (present perfect progressive) The Cosmos had been winning. (past perfect progressive) The Cosmos will be winning. (future progressive) The Cosmos will have been winning. (future perfect progressive)

7j

Principal parts of irregular verbs We call a verb like “eat” an irregular verb. Any verb that changes internally to form the past participle is an irregular verb.

*See page 523 (top), which discusses how a present tense may express future time.

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Present Tense

Past Tense

Past Participle

Present Participle

eat begin blow break burst catch choose come do drink drive fall find fly freeze give go grow know lay (place) lie (rest) ring raise rise run set sit speak steal swim take throw wear write

ate began blew broke burst caught chose came did drank drove fell found flew froze gave went grew knew laid lay rang raised rose ran set sat spoke stole swam took threw wore wrote

eaten begun blown broken burst caught chosen come done drunk driven fallen found flown frozen given gone grown known laid lain rung raised risen run set sat spoken stolen swum taken thrown worn written

eating beginning blowing breaking bursting catching choosing coming doing drinking driving falling finding flying freezing giving going growing knowing laying lying ringing raising rising running setting sitting speaking stealing swimming taking throwing wearing writing

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Chapter 8: Verbals

8a

A verbal is a word formed from a verb. Skiing can be dangerous. We could hear our neighbors arguing. Bonnie and Clyde worked hard to succeed.

8b The three kinds of verbals are gerunds, participles, and infinitives. 8c

A gerund acts like a noun. Smoking is not allowed in many stores. Traveling by train can be fun. Mark’s favorite sport is boating. A gerund ends in “ing.” Nureyev’s dancing is terrific. Flying is the fastest way to get there. A phrase that begins with a gerund is called a gerund phrase. Paying bills on time is a good habit. Leaving my friends made me sad.

8d A participle acts like an adjective. The police stopped the speeding car. The tired children were sent to bed. A present participle ends in “ing.” A priest comforted the dying woman. Running, the girl caught up with her friends. Note: A present participle looks like a gerund because they both end in “ing.” A present participle, however, is used as an adjective, not as a noun. A past participle usually ends in “d,” “ed,” “t,” “n,” or “en.” Used clothing is cheaper than new clothes. Woody left written instructions for his assistant.

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A phrase that begins with a participle is called a participial phrase. Getting off the elevator, I met a friend. Questioned by the police, several witnesses described the robbery. 8e

An infinitive is used as a noun or an adjective or an adverb. Franz loves to dance. (noun) Our candidate has the ability to win. (adjective) Lisa practices every day to improve. (adverb) An infinitive usually begins with “to,” but not always. Sally wants to know if you need a ride. Help me wash my car. (Or: Help me to wash my car.) A phrase introduced by an infinitive is called an infinitive phrase. His only desire was to save money. (infinitive phrase used as a noun) There must be a way to solve this problem. (infinitive phrase used as an adjective) The doctor is too busy to see you now. (infinitive phrase used as an adverb)

8f

Gerunds may be present or perfect. Good cooking is her specialty. (present) Your having arrived on time saved me. (perfect) A gerund in the present form refers to an action happening at the same time as the action of the main verb. Swimming is fun. Running a mile tired him out. Taking driving lessons will help you drive better. A gerund in the perfect form refers to an action that was completed before the time of the main verb. He believes his recovery is a result of his having prayed. Our having read the book made the movie boring.

8g

Participles may be present, past, or perfect. The woman sitting on the couch is my mother. (present) Warned by his doctor, Jack began to exercise. (past) Having been recognized, Elton John was mobbed by his fans. (perfect) A present participle refers to action happening at the same time as the action of the main verb. present

Smiling broadly, the president answers questions from the audience. past

Smiling broadly, the president answered questions from the audience.

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GRAMMAR AND USAGE REFRESHER • 495 present

Holding up his hands, the teacher is asking for silence. past

Holding up his hands, the teacher asked for silence. A past participle sometimes refers to action happening at the same time as the action of the main verb. Irritated by his sister, Raphael yelled at her. Dressed up, Tom looks like a new man. A past participle sometimes refers to action that happened before the action of the main verb. Burned by the sun, Mary is suffering. Awakened by the noise, we looked outside. The perfect participle always refers to action occurring before the action of the main verb. Having finished work, we can leave. Having seen that movie, we went somewhere else. Having left home in a hurry, Michael forgot his raincoat. 8h Infinitives may be present or perfect. Albert likes to read all day. (present) Tina was supposed to have brought the money. (perfect) The present infinitive shows an action occurring at the same time as the action of the main verb. I am tr ying to finish this puzzle. (both present) Jerry looked around to see who was there. (both past) Dana will call to ask you for some advice. (both future) The present infinitive may indicate action or a state of being at some future time. I hope to see you again. I expect to be there in an hour. He intended to write to us. An infinitive is never used in a subordinate clause which begins with “that.” I expect everyone to remain seated. I expect that everyone will remain seated. (Not: I expect that everyone to remain seated.) The perfect infinitive expresses action occurring before that of the main verb. I am sorry not to have met you before. He claims to have seen a flying saucer.

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Avoid using the perfect infinitive after main verbs in the past or past perfect tense. I had expected to receive my mail today. (Not: I had expected to have received . . . ) They hoped to join us for dinner. (Not: They hoped to have joined us . . . ) Mike would have liked to ask Alice for a date, but he was too shy. (Not: Mike would have like to have asked Alice . . . )

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Chapter 9: Mood and Voice

9a

Mood The three moods that a verb may express are indicative, imperative, and subjunctive.

9b The indicative mood indicates that the action or state is something believed to be true. I am the greatest. She sings beautifully. The indicative mood is used in asking a question. Are you Mr. Feldman? Does Tom want to watch “Saturday Night Live?” 9c

The imperative mood expresses a command or a request or a suggestion. Answer the telephone. (command) Give me a napkin, please. (request) Tr y turning the handle the other way. (suggestion) The imperative mood is not only more emphatic than the indicative mood—it is more quickly and easily understood. Give me that letter. (imperative) I would appreciate it if you would give me that letter. (indicative)

9d The subjunctive mood is often used to express a wish or a condition that is not real—that is, contrar y to fact. I wish the weather were nicer. If this paint were dry, we could sit on the bench. Debbie suggested that Carol stay at her apartment. Carl asked that Stan agree to pay for the damage. The subjunctive mood is also used to express purpose or intention. Connie said that she would visit her mother at Easter. (Not: Connie said that she will visit her mother at Easter.) We made box lunches so that we would have food for the trip. (Not: We made box lunches so that we had food for the trip.) The subjunctive mood is mainly indicated by two forms of the verb “to be.” The forms are “be” and “were.” Be good. If I were president, I’d nationalize the oil industry.

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The present subjunctive uses “be” for all three persons, both singular and plural. I be, you be, he be, we be, they be I have one wish—that I be president some day. Mrs. Diggs insists that you be given a bonus. I asked that the child not be punished. The judge ordered that the tenants be allowed to stay.

The more common form of the subjunctive is the past subjunctive form “were” for all three persons, both singular and plural.

If

I you he we they

were here, everything would be all right.

The subjunctive mood for verbs other than “to be” is formed by using the present tense first person singular form for all persons. Mary suggested that Ronald keep an extra pair of eyeglasses. The umpire insisted that the manager leave the field. 9e

Choosing between the subjunctive and indicative mood. One should show how he sees a situation: contrar y to fact or within the realm of possibility. He does this by choosing either the subjunctive mood or the indicative mood. If his statement be true, this is a case of fraud. (subjunctive) (One indicates that he thinks it is highly improbable that the statement is true.) If his statement is true, this may be a case of fraud. (indicative) (The writer indicates that it is quite possible that the statement may be true.) If he were at the meeting, he would . . . ) (subjunctive) (The speaker tells the listener that the man is not at the meeting.) If he was at the meeting, he would have been able to speak to the point. (indicative) (Perhaps the man was at the meeting; one doesn’t know.) Had the first payment been made in April, the second would be due in September. (subjunctive) (The speaker indicates that the payment was not made in April.) If the first payment was made in April, the second will be due in September. (indicative) (Perhaps it was made; perhaps not—the speaker doesn’t know.) Do not use “would have” instead of “had” in “if ” clauses to express the past perfect tense of the subjunctive. If he had worked harder, he would have a better job. (Not: If he would have worked harder . . . )

9f

Voice A verb is either in the active voice or in the passive voice.

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9g

A verb in the active voice indicates that the subject performs an action. Maggie reads every night before going to sleep. The fire burned the entire house. A verb in the active voice stresses the subject or actor rather than the action.

9h A verb in the passive voice indicates that something is being done to the subject. The children were given lunches to take to school. The television was turned off by my dad. A verb in the passive voice stresses the action rather than the actor. 9i

All transitive verbs—verbs whose action affects something or someone—can be used in the passive voice. Johnny Bench caught the ball. (active) The ball was caught by Johnny Bench. (passive)

9j

To form the passive, the object of the transitive verb in the active voice is moved ahead of the verb, thus becoming the subject. A form of “to be” is added to the main verb. The subject of the active sentence is either left out or expressed in a prepositional phrase. subject

active verb

direct object

The tow truck pulled the car out of the ditch. (active voice) subject

passive verb

prepositional phrase

The car was pulled out of the ditch by the tow truck. (passive voice) 9k If the active sentence has an indirect object as well as a direct object, either the indirect object or the direct object may be the subject of the passive sentence. active verb

indirect object

direct object

Tom gave his sister a kitten. (active) subject

passive verb

A kitten was given by Tom to his sister. (passive) subject

passive verb

Tom’s sister was given a kitten by Tom. (passive) 9l

The passive voice is appropriate to express an action when the actor is unknown. The door had been locked before we arrived. Note: In general, avoid the passive voice for clearer, more forceful sentences.

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Chapter 10: Modifiers—Adjectives, Adjective Phrases and Clauses

10a Modifiers A modifier adds information to another word in the sentence. Blue flowers were growing in the field. (The adjective “blue” adds color to the noun “flowers.”) Vera paints beautifully. (The adverb “beautifully” tells how Vera paints.) 10b Modifiers may be a word, a phrase, or a clause. Billy put on a clean shirt. (word) The wristband of her watch was broken. (phrase) Andy liked the painting that was done by his friend. (clause) There are various types of modifiers. Jill brought us fresh fruit. (adjective as modifier) Bob’s friends greeted him warmly. (adverb as modifier) Rudy enjoyed the ride from Birmingham to Atlanta. (adjective phrase as modifier) The rent will increase after this month. (adverb phrase as modifier) Louise holds two jobs because she supports her sons in college. (subordinate clause as adverbial modifier) The houses where American presidents were born are museums. (subordinate clause as adjectival modifier) 10c Adjectives modify nouns The six kinds of adjectives are the following: Limiting: Many children are bused to school. Numerical: Four days have passed since I saw her. Descriptive: Striped wallpaper hung in the hall. Proper: American and Russian flags lined the parade route. Pronoun: My book has a torn cover. Article: A letter has arrived.

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10d Articles The articles “a” and “an” (indefinite articles) indicate that the noun they modify is an example of a general type. A dove symbolizes peace. (any dove) A doctor saves lives. (any doctor) An ambulance brings people to hospitals. (any ambulance) Note: Do not use the articles “a” or “an” after “kind of,” “type of,” or “sort of.” A mango is a kind of fruit. (Not: . . . a kind of a fruit.) The Citation is a new type of car. (Not: . . . a new type of a car.) That sound gives me a sort of weird feeling. (Not: . . . a sort of a weird feeling.) The article “the” (definite article) indicates that the noun it modifies is a par ticular noun. The winner received ten thousand dollars. (specific person) The lamp over there is sold. (specific thing) 10e Single adjectives and compound adjectives A single adjective usually comes immediately before the word it modifies. Help me carry this heavy package. A compound adjective consists of two or more words ser ving as a single adjective. The drought made the earth bone dr y. My dictionary is up to date. When a compound adjective comes before a noun, the words are joined by a hyphen. Woody Allen was my next-door neighbor. A large-scale map is hanging on the wall. When the modifying words follow a noun, they are not hyphenated, unless they are normally hyphenated compounds. This book is well written. My new watch is self-winding. (normally hyphenated) When two or more adjectives come before a noun but do not act jointly, they are not hyphenated. Jim was wearing a white silk shirt. I’ve had a long, hard day. Note: If the word “and” can be inserted between two adjectives that come before a noun without destroying the meaning of the sentence, put a comma in between the two adjectives; otherwise, do not. Miss Cameron is a kind, generous person. (kind and generous) Show us your new suit. (Not: . . . your, new suit.)

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10f

Two or more adjectives may follow the word they modify to make the sentence read more smoothly. The children, tired and hungr y, were difficult to control.

10g Most adjectives may show greater or lesser degrees of their characteristic quality. Today was cold. (characteristic quality) Tomorrow will be colder than today. (greater) The day after will be the coldest. (still greater) Yesterday was less cold than today. (lesser) The day before was the least cold this week. (lesser still) Some adjectives do not show comparison. Jennifer is pregnant. (She cannot be more or less pregnant.) This salad dressing is perfect. (Not: . . . is more or less perfect.) 10h The three degrees of comparison are positive, comparative, and superlative. Tania is happy. (positive degree) Lenny is happier than Frank. (comparative degree) Wayne is the happiest of all. (superlative degree) The positive degree simply names the quality expressed by an adjective. I like spicy food. The comparative degree indicates that the quality described by an adjective exists in one person to a greater or lesser degree than in another person or thing. Susan looks older than Liz. (greater) Marlo was more excited than her brother. (greater) This street is less clean than the one where I live. (lesser) The greater form of the comparative degree is formed by adding “er” to the positive degree or by inserting “more” before the positive form. rich er richer rich more more rich The lesser form of the comparative degree is formed by inserting “less” before the positive form. rich less less rich Note: Use the comparative degree when comparing only two things. The superlative degree indicates that the quality described by an adjective exists in the greatest or least degree in one person or thing. Rufus is the friendliest dog I know. (greatest) Florence seems the least ner vous of us all. (least) Note: Use the superlative degree when comparing more than two things.

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10i

Some adjectives do not follow the regular methods of forming their comparative and superlative degrees. Positive degree

Comparative degree

Superlative degree

good

better

best

bad

worse

worst

little

less, lesser

least

(A dictionary will provide the irregular comparisons of such adjectives.) Most adjectives of three syllables or more are compared by the use of “more” and “most,” rather than by the endings “er” and “est.” Tim is more capable of managing a business than Jon. Alma is the most wonderful girl I know. 10j

Avoid double comparisons which are formed by adding both “more” or “most” and “er” or “est.” Alan is the brightest little boy. (Not: . . . the most brightest . . . ) Eric is a better eater than his brother. (Not: . . . a more better eater . . . )

10k When two things are compared, both things should be clearly accounted for. These clothes look cleaner than those (clothes). George looks older than he used to. An ellipsis is the leaving out of one or more words that are grammatically important but that are understood by the reader. Harvey plays soccer better than I (do). While (he was) waiting for the pitch, Al Bumbry clenched the bat tightly. Incomplete subordinate clauses that cause confusion, similar to the confusion caused by dangling modifiers, may be corrected by supplying the missing words. Margaret’s dress was torn while she was climbing over the fence. (Not: Margaret’s dress was torn while climbing over the fence.) Use the word “other” or “else” to separate the thing being compared from the rest of the group of which the word is a part. This car gets better mileage than all the other cars. Mar y Beth is more beautiful than anyone else around. 10l

Infinitives, infinitive phrases, participles, and participial phrases may act as adjectives. Mr. Garcia is the man to know if you want a bank loan. (infinitive as adjective) This is a day to remember always. (infinitive phrase as adjective) Screaming, Nancy woke up from her nightmare. (present participle as adjective) Covering his face, the defendant walked past the reporters. (participial phrase as adjective)

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10m Infinitive and participial phrases that begin a sentence must be able to refer, both logically and grammatically, to the subject of the main clause. To qualify for the job, you need a high school diploma. (Not: To qualify for the job, a high school diploma is needed. A “high school diploma” cannot apply for the job.) Rushing to finish, Tina made some errors. (Not: Rushing to finish, some errors were made by Tina. “Errors” cannot rush to finish.) 10n Infinitive and participial phrases are called dangling modifiers if they cannot logically and grammatically attach to the subject of the main clause. To apply for a credit card, an application form must be filled out. (infinitive phrase as dangling modifier) Being an only child, my parents spoiled me. (participial phrase as dangling modifier) Sentences with dangling modifiers may be corrected either by supplying the subject that the phrase can sensibly modify or by changing the phrase to an introductory adverbial clause. To apply for a credit card, one must fill out an application. (Or: When one applies for a credit card, an application form must be filled out.) Being an only child, I was spoiled by my parents. (Or. Because I am an only child, I was spoiled by my parents.) 10o A prepositional phrase may act as an adjective. The violent storm damaged the roof of our house. Her leaving without saying a word irritated me. (also considered a gerund phrase) 10p A subordinate clause may act as an adjective. Thanks for the present that you gave me. The woman who can help you is not at her desk. This ring, which belonged to my grandmother, is valuable. The building where they used to live is being torn down. There is never a time when Ed isn’t busy. Subordinate clauses that act as adjectives may state essential information or nonessential information. The train that you need to take is leaving from Track 12. (information essential to describe which train) Peter loves his car, which he hasn’t finished paying for. (information that is nonessential to describe which car) 10q Restrictive and nonrestrictive clauses Restrictive clauses, which contain essential information, are not set apart by commas. The secondhand radio that I bought for five dollars works beautifully. (restrictive clause) Nonrestrictive clauses, which contain secondar y information that is not essential to the sentence, are set off by commas. My friend Dina, whom I’ve known for years, wants me to visit her. (nonrestrictive clause)

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10r “Whose” is the possessive form for the relative pronouns “who,” “which,” and “that.” The boy whose father died had to get a job. The dog whose leg was broken runs well now. Mr. Temple, whose wife is a ballerina, teaches French. The book whose cover is damaged is half price. 10s A word, phrase, or clause should be placed as close as possible to the word it modifies. Give me a glass of cold beer. (Not: Give me a cold glass . . . ) We need someone with experience to cook breakfast. (Not: We need someone to cook breakfast with experience.) Grant wore a felt hat that was obviously too small on his head. (Not: Grant wore a felt hat on his head that was obviously too small.) 10t

A misplaced modifier is a word, phrase, or clause that is misplaced in the sentence so that it modifies the wrong word. Wrong: Mrs. Kent was injured while preparing her husband’s dinner in a horrible manner. Right:

Mrs. Kent was injured in a horrible manner while preparing her husband’s dinner.

Wrong: The old farmer went to the barn to milk the cow with a cane. Right:

The old farmer with the cane went to the barn to milk the cow.

Wrong: The flames were extinguished before any damage was done by the Fire Department. Right:

The flames were extinguished by the Fire Department before any damage was done.

10u Squinting modifiers are modifiers that are misplaced so that the reader cannot tell if the word, phrase, or clause modifies the words immediately before the modifier or immediately after. Wrong: Henry said today he would wash his car. Right:

Today Henry said he would wash his car. (Or: Henry said he would wash his car today.)

Wrong: The dentist told him frequently to use dental floss. Right:

The dentist frequently told him to use dental floss. (Or: The dentist told him to use dental floss frequently.)

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Chapter 11: Modifiers (continued)— Adverbs, Adverbial Phrases and Clauses

11a Adverbs modify verbs, adjectives, and adverbs. Don runs slowly. (modifies verb) Emily is an extremely gifted pianist. (modifies adjective) Eric Heiden skates incredibly well. (modifies adverb) 11b The five kinds of adverbs are classified by the questions they answer. How? Adverbs of manner. She sings well. He speaks clearly. Where? Adverbs of place or direction. Take me home. She was just here. He went out. When? Adverbs of time. Bring it immediately. I’ll see you tomorrow. How much? Adverbs of degree or measure. That’s enough. A little more, please. Why? Adverbs of cause, reason, or purpose. He left because he was afraid. I have ten dollars, so we can go out. 11c The following words can be either adjectives or adverbs, depending on their use. above

fast

only

better

first

slow

cheap

hard

well

deep

long

early

much

The sign said to drive slow. (adverb) Slow drivers can be dangerous. (adjective) Mark Spitz can swim better than I can. (adverb) Lucy feels better now. (adjective)

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11d Distinguish carefully when an adverb should follow a linking verb and when a predicate adjective should be used to follow the linking verb. Sharon looks bad. (predicate adjective meaning that Sharon doesn’t look healthy) Miguel looks badly. (adverb meaning that Miguel is doing a poor job looking for something) Carmen smells sweet. (predicate adjective meaning that Carmen has a sweet scent) Roses smell sweetly. (adverb incorrectly meaning that roses sniff the air sweetly!) 11e While speaking, one may incorrectly drop the “ly” ending from common adverbs. I’m real glad you called. (Correct: I’m really glad you called.) He sure is lucky. (Correct: He surely is lucky.) Do not drop the “ly” ending unless a shorter form is correct. I bought it cheaply. (Or: I bought it cheap.) Come quickly! (Or: Come quick!) The adverbs “hardly,” “scarcely,” “only,” and “barely” should not be used with a negative verb construction. Ernie has hardly any free time. (Not: Ernie hasn’t hardly any free time.) Rose and I have scarcely worked this week. (Not: Rose and I haven’t scarcely worked this week.) 11f

An adverb may show greater or lesser degrees of its characteristic quality. Peter arrived early. Adam came earlier than Peter. Amy came earliest of all. The positive degree simply names the quality expressed by an adverb. Stephanie runs quickly. The comparative degree indicates that the quality described by an adverb exists for one person or thing to a greater or lesser degree than for another person or thing. New air conditioners run more efficiently than old ones. Nat draws less well than Monica. The comparative degree of adverbs is formed by inserting “more” or “less” before the positive degree form, unless there is an irregular form for the comparative degree. Charles works more diligently than Mark. Barbara gets angry less often than Steven. This stereo sounds better than mine. (irregular form)

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The superlative degree indicates the quality described by the adverb exists in the greatest or least degree for one person or thing. Ben works most carefully when someone is watching. Elaine explained the problem the most clearly. His was the least carefully written report. The superlative degree of adverbs is formed by inserting “most” or “least” before the positive degree form. Who was voted “most likely” to suceed”? Tracy Austin played least skillfully during the first set. When two persons or things are being compared, the comparison should be clear. I love chocolate more than Umberto does. (Not: I love chocolate more than Umberto. Such an incomplete comparison might be interpreted to mean that I love chocolate more than I love Umberto.) 11g An infinitive or an infinitive phrase may be used as an adverb. Robert was willing to go. (infinitive used as adverb) I am writing to explain my behavior last night. (infinitive phrase used as adverb) 11h A prepositional phrase may be used as an adverb. We left for the weekend. The old man sat on the park bench. The coach supported his team in ever y way. 11i

A subordinate clause may be used as an adverb. Mrs. Maurillo forgot her umbrella when she left. Because they cooperated with him, the president thanked several members of Congress.

11j

An adverb or an adverbial phrase should be placed as close as possible to the word it modifies. Joanne worked without complaining while her husband went to school. (Not: Joanne worked while her husband went to school without complaining.) Note how an adverbial misplacement may change the meaning of a sentence. The room can be painted only by me. (not by anyone else) The room can only be painted by me. (not wallpapered) Only the room can be painted by me. (not the outside of the house)

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11k An adverbial clause may be placed either at the beginning of a sentence or, in its natural order, after the main clause. After you have read this letter, you will understand my reasons. You will understand my reasons after you have read this letter. Note: An adverbial clause is followed by a comma when it is used to introduce a sentence. 11l

Adverbial phrases and clauses should be placed so that only one meaning is possible. After the movie we all agreed to go for some ice cream. (Or: We all agreed to go for some ice cream after the movie. (Not: We all agreed after the movie to go for some ice cream.) Ask Kay to call me when she gets in. (Or: When she gets in, ask Kay to call me). (Not: Ask Kay when she gets in to call me.)

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Chapter 12: Connectives

12a A connective joins one part of a sentence to another part. Phillip and Dennis are giving a concert tonight. (The connective “and” joins the two parts of the compound subject.) Did you go out, or did you stay home last night? (The connective “or” joins the two independent clauses.) The banks are closed because today is a holiday. (The connective “because” joins the main clause to the subordinate clause.) The investigation of the robbery has been completed. (The connective “of” joins the noun “robbery” to the noun “investigation.”) 12b A connective may be a preposition, a conjunction, an adverb, or a pronoun. Josie left her scarf on the bus. (preposition) Mr. Fernandez campaigned for the presidency, but he lost. (conjunction) Kevin looked back because someone was shouting. (conjunction) Ernie left his home an hour ago; therefore, he should be here any minute. (adverb) The letter that was mailed this morning should arrive tomorrow. (pronoun) 12c Prepositions as connectives A preposition may be a word or a compound. A compound consists of two or more words that function as one word. Come over here. (word) Women live longer than men according to statistics. (compound) 12d A preposition joins a noun or pronoun to the rest of the sentence. prep.

One of the windows is broken. (noun) prep.

Josh is worried about his health. (noun) prep.

These bags have nothing in them. (pronoun) Choosing the correct preposition is often based on idiomatic usage—that is, the way English is used, whether or not it contradicts strict grammatical rules.

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12e Some commonly used prepositional idioms are the following: absolve abstain accede accommodate accompanied accompanied account account acquit adapted adapted adept adequate adequate agree agree amenable angry angry annoyed annoyed appreciative averse basis capable concur concur confer confer conform correspond correspond differs differs disappointed disappointed enter enter excepted exempt expect expect familiar familiar free free identical ignorant incompatible independent infer involved involved liable necessity

from from to to by with for to of to from in to for to with to with at by with of to for of with in with about to to with from with in with into upon from from from of to with of from with of with of from in with to for

[blame] [drinking] [a request] [a situation] [a lady (a person)] [applause (a thing)] [one’s actions] [one’s superior] [a crime] [his requirements] [a novel] [selling a product] [the demand] [her needs] [a proposal (an idea)] [the teacher (a person)] [an offer] [my cousin (a person)] [a remark (a thing)] [the noise (a thing)] [the child (a person)] [their efforts] [hard work (an idea)] [agreement] [getting high marks] [the mayor (a person)] [the decision (an idea)] [someone (a person)] [something (a thing)] [the rules] [what I said (a thing)] [his lawyer (a person)] [her sister (a person)] [what was done (a thing)] [you (a person)] [the result (a thing)] [an agreement] [a career] [further responsibility] [taxes] [your investment (a thing)] [his assistant (a person)] [me (a person)] [the proceedings (a thing)] [his wife (a person)] [her nagging (a thing)] [something else] [his rights] [fellow workers] [his relative] [a statement] [a project (a thing)] [a friend (a person)] [damages (a thing)] [food (a thing)]

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necessity proficient profit responsible responsible talk talk variance wait wait worthy 12f

of in by to for to with with at for of

[avoiding trouble (doing something)] [a skill] [knowledge] [the owner (a person)] [paying a debt (a thing)] [the group (one person talks)] [my friends (all talk)] [another] [the church (a place)] [your uncle (a person)] [consideration]

Prepositions should not be used needlessly. Where is your brother? (Not: Where is your brother at?) Where are you going? (Not: Where are you going to?) Pete started on another project. (Not: Pete started in on another project.) We agreed to divide the housework. (Not: We agreed to divide up the housework.) Prepositions are sometimes left out by mistake. Irene talked to me about her new job and about why she left her old one. (Not: Irene talked to me about her new job and why. . . . ) Dr. Rosen was puzzled by and concerned about Ellen’s nightmares. (Not: Dr. Rosen was puzzled and concerned about. . . . ) Note: Two different prepositions are needed for this last sentence.

12g Conjunctions as connectives A conjunction is a word that joins words, phrases, clauses, or sentences. Nixon and Agnew ended their political careers by resigning. (words joined) The mouse ran out of the kitchen and into the living room. (phrases joined) Casino gambling in Atlantic City has helped some, but it has hurt others. (clauses joined) Sally has the ability to do the job; however, she has too many personal problems. (sentences joined) 12h Conjunctions are coordinate, correlative, or subordinate. A coordinate conjunction and a correlative conjunction connect grammatical elements of equal rank. A subordinate conjunction connects grammatical elements of unequal rank. 12i

Coordinate conjunctions include the following words in order to connect two equal elements. and, but, or, nor, so, yet On our vacation we will go to Boston or to Cape Cod. (two phrases) My two favorite colors are blue and green. (two words) I told Stanley that I couldn’t leave my house, so he should come over tonight. (two subordinate clauses) Phil was eager to try the new restaurant, but he moved away before trying it. (two independent clauses)

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12j

Correlative conjunctions include the following word pairs in order to connect two equal elements. either . . . or, neither . . . nor, not only . . . but also, both . . . and, if . . . then, since . . . therefore Take either the dark meat or the light meat. (two words) Not only has Rick quit school, but he has also left town. (two independent clauses) Both the Baltimore Orioles and the Pittsburgh Pirates won the pennant in 1979. (two words) I have seen her neither in the movies nor on television. (two phrases) Note: The correlative conjunctions “neither . . . nor” should never be written “neither . . . or.” Each member of the pair of correlative conjunctions must be followed by the same grammatical construction. same construction

Woody Allen is not only a good comedian but also a good film director. different construction

(Not: Woody Allen not only is a good comedian but also a good film director.) same construction

Either we should spend the night here or we should leave right now. different construction

(Not: Either we should spend the night here or leave right now.) 12k Conjunctive adverbs A conjunctive adverb may be considered a type of coordinate conjunction. Conjunctive adverbs include the following words which ser ve to connect two equal elements. therefore, however, consequently, accordingly, furthermore, besides, moreover, nevertheless, still Although the clause introduced by a conjunctive adverb is grammatically independent, it is logically dependent on the preceding clause for complete meaning. A storm knocked down our electric wires; therefore, we had to eat by candlelight. A bad traffic accident ahead of us caused us to be delayed; nevertheless, we made the party on time. You have not paid your rent for six months; accordingly, I am going to see a lawyer. Independent clauses joined by a conjunctive adverb should be separated by a semicolon (;) or a period. Frank and Marty delayed their vacation one week; consequently, I was able to join them. The judge awarded custody of the child to its mother. Moreover, the judge set strict guidelines for visiting privileges. Certain phrases may act as conjunctive adverbs. Eunice wanted to buy a fur coat; on the other hand, she was trying to save money for a car. We saw many interesting towns and cities on our tour. In addition, we met several nice people.

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12l

Join only the same parts of speech with coordinate conjunctions or with correlative conjunctions. Faulty parallelism will result if dif ferent parts of speech are combined. Correct: Jim’s day consisted of waking up early, working all day, and going back to bed. (three gerund phrases) Faulty:

Jim’s day consisted of waking up early, working all day, and then to go back to bed. (two gerund phrases combined with an infinitive phrase)

Correct: The president’s plan was a disappointment not only to the leaders of big business, but also to the leaders of organized labor. (two prepositional phrases) Faulty:

The president’s plan was a disappointment not only to the leaders of big business, but also the leaders of organized labor. (one prepositional phrase and one noun)

12m Connecting elements of unequal rank A less important idea should be put into a subordinate clause; the more important idea should be expressed in the main or independent clause. main idea

subordinate idea

Bill is going to work for his father, although he was offered other jobs. 12n Subordination may be introduced by a subordinate conjunction, by a relative pronoun, or by a relative adverb. Eva will want to go straight to bed after she comes back from her exercise class. (subordinate conjunction) I bought the sneakers that you wanted. (relative pronoun) We saw the house where they filmed “Gone with the Wind.” (relative adverb) A subordinate conjunction introduces an adverbial clause. My mother can knit a sweater while she watches television. (adverbial clause tells when) Tell me what he looks like so that I’ll recognize him. (adverbial clause tells why) 12o Some relative pronouns introduce adjective clauses. Everyone wants a job that he likes. The woman who walked across the United States has written a book about her experience. Bobby gave Connie a new tennis racket, which she needed. Other relative pronouns introduce noun clauses. Tell me what you did. This book has whatever you want to know about scuba diving. Invite whomever you like. 12p A relative adverb introduces an adjective clause. Do you remember the night when we locked ourselves out of the house? Chris will be at the place where we met him last time.

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Chapter 13: Correct Usage: Choosing the Right Word

“The difference between the right word and the almost-right word is the difference between lightning and the lightning bug (firefly).” —Mark Twain

A, an. The indefinite article a is used before a consonant sound; the indefinite article an is used before a vowel sound. Say a plan, an idea. Accept, except. Accept means to receive; except when used as a verb means to leave out. (We accepted the gift. Pedro’s name was excepted from the honor roll.) The word except is used most often as a preposition. Everyone went except me. Affect, effect. Affect is a verb which means to influence. (Winning the sweepstakes will affect his attitude.) Effect, as a noun, means an influence. (Smoking has an effect on one’s health.) Effect, as a verb means to bring about. (The teacher’s praise effected a change in the student.) Affected, as an adjective, has the meaning of false. (She had an affected way of speaking.) Aggravate, irritate. Aggravate means to make worse. (Drinking iced water will aggravate your cold.) Irritate means to annoy or exasperate. (Mary’s continuous chattering irritated me.) Ain’t. Do not use this expression. Already, all ready. Already means before or by a certain time. (Mike said that he had already done the job.) All ready means completely ready. (When the buzzer sounded, the horses were all ready to start running.) All right, alright. The only correct spelling is all right. Altogether, all together. Altogether means entirely, wholly. (Jane is altogether too conceited to get along with people.) All together means as a group. (After the explosion, the boss was relieved to find his workers all together in front of the building.) Among, between. Among is used with more than two persons or things. (The manager distributed the gifts among all of the employees.) Between is used only with two persons or things. (The steak was divided between the two children.) Amount, number. Amount is used to refer to things in bulk. (The war costs a great amount of money.) Number is used to refer to things that can be counted. (A large number of pupils attend this school.) And etc. This is incorrect. The abbreviation etc. stands for the Latin et cetera. The et means and; the cetera means other things. It is wrong to say and etc. because the idea of and is already included in the etc. Anyways, anywheres, ever ywheres, somewheres. These expressions are not correct. Omit the final s after each. As, like. As, used as a conjunction, is followed by a verb. (Please do it as I told you to.) Like may not be used as a conjunction. If it is used as a preposition, it is not followed by a verb. (This ice cream looks like custard.) Awful. See Terrific, terrible. Being that. Being that is incorrect for since or because. (Since you are tired, you ought to rest.) Beside, besides. Beside means alongside of; besides means in addition to. (Nixon sat beside Autry at the baseball game.) (There is nobody besides her husband who understands Ann.)

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Between. See Among. Bring, take. Consider the speaker as a starting point. Bring is used for something carried in the direction of the speaker. (When you return from lunch, please bring me a ham sandwich.) Take is used for something carried away from the speaker. (If you are going downtown, please take this letter to the post office.) Bunch. Bunch means cluster. Do not use bunch for group or crowd. (This is a large bunch of grapes.) (A crowd of people were at the scene of the accident.) But that, but what. Do not use these expressions in place of that in structures like the following: I do not question that (not but that) you are richer than I am. Can’t hardly. Don’t use this double negative. Say can hardly. Continual, continuous. Continual means happening at intervals. (Salesmen are continually walking into this office.) Continuous means going on without interruption. (Without a moment of dry weather, it rained continuously for forty days and forty nights.) Could of. Do not use for could have. Data. Although data is the plural of datum, idiom permits the use of this word as a singular. Some authorities still insist on Data are gathered rather than Data is gathered or these data rather than this data. Most persons in computer programming now say Data is gathered or this data. Deal. Do not use this term for arrangement or transaction. (He has an excellent arrangement (not deal) with the manager.) Different from, different than. Different from is correct. Different than is incorrect. (His method of doing this is different from mine.) Discover, invent. Discover means to see or learn something that has not been previously known. (They say the Vikings, not Columbus, discovered America.) Invent means to create for the first time. (William S. Burroughs invented the adding machine.) Disinterested, uninterested. Disinterested means without bias. (An umpire must be disinterested to judge fairly in a baseball game.) Uninterested means not caring about a situation. (I am totally uninterested in your plan.) Doesn’t, don’t. (does not).

Doesn’t means does not; don’t means do not. Do not say He don’t (do not) when you mean He doesn’t

Due to. At the beginning of a sentence, due to is always incorrect. Use, instead, on account of, because of, or a similar expression. (On account of bad weather, the contest was postponed.) As a predicate adjective construction, due to is correct. His weakness was due to his hunger. Each other, one another. Each other is used for two persons. (The executive and his secretary antagonize each other.) One another is used for more than two persons. (The members of the large family love one another.) Effect. See Affect. Enthuse. Do not use this word. Say enthusiastic. (The art critic was enthusiastic about the painting.) Equally as good. This expression is incorrect. Say, instead, just as good. (This car is just as good as that.) Farther, further. Farther is used for a distance that is measurable. (The farmer’s house is about 100 yards farther down the road.) Further is used to express the extension of an idea. (A further explanation may be necessary.) Fewer, less. Fewer applies to what may be counted. (Greenwich Village has fewer conservatives than liberals.) Less refers to degree or amount. (Less rain fell this month than the month before.) Flout, flaunt. Flout means to mock or insult. (The king flouted the wise man when the latter offered advice.) Flaunt means to make a pretentious display of. (The upstart flaunted his diamond ring.) Further. See Farther. Get. Get means to obtain or receive. Get should not be used in the sense of to excite, to interest, or to understand. Say: His guitar playing fascinates (not gets) me. Say: When you talk about lifestyles, I just don’t understand (not get) you. Good, well. Do not use the adjective good in place of the adverb well in structures like the following: John works well (not good) in the kitchen. Jim Palmer pitched well (not good) in last night’s game.

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Graduate. One graduates from, or is graduated from, a school. One does not graduate a school. (The student graduated [or was graduated] from high school.) Had of.

Avoid this for had. Say: My father always said that he wished he had (not had of ) gone to college.

Hanged, hung. When a person is executed, he is hanged. When anything is suspended in space, it is hung. Hardly. See Can’t hardly. Healthful, healthy. Healthful applies to conditions that promote health. Healthy applies to a state of health. Say: Stevenson found the climate of Saranac Lake very healthful. Say: Mary is a very healthy girl. If, whether. Use whether—not if—in structures that follow verbs like ask, doubt, know, learn, say. Say: Hank Aaron didn’t know whether (not if ) he was going to break Babe Ruth’s homerun record. Imply, infer. The speaker implies when he suggests or hints at. (The owner of the store implied that the patron stole a box of toothpicks.) The listener infers when he draws a conclusion from facts or evidence. (From what you say, I infer that I am about to be discharged.) In, into. In is used to express a location, without the involvement of motion. (The sugar is in the cupboard.) Into is used to express motion from one place to another. (The housekeeper put the sugar into the cupboard.) In regards to. This is incorrect. Say in regard to or with regard to. Invent. See Discover. Irregardless. Do not use irregardless. It is incorrect for regardless. (You will not be able to go out tonight regardless of the fact that you have done all of your homework.) Its, it’s.

Its is the possessive of it; it’s is the contraction for it is.

Kind of, sort of. Do not use these expressions as adverbs. Say: Ali was quite (not kind of or sort of ) witty in his postfight interview. Kind of a, sort of a. Omit the a. Say: What kind of (not kind of a or sort of a) game is lacrosse? Lay, lie.

See “Principal Parts of Irregular Verbs”—page 491.

Learn, teach. Learn means gaining knowledge. Teach means imparting knowledge. Say: He taught (not learned) his brother how to swim. Leave, let. The word leave means to depart. (I leave today for San Francisco.) The word let means to allow. (Let me take your place.) Less, fewer.

See Fewer, less.

Liable, likely. Liable means exposed to something unpleasant. (If you speed, you are liable to get a summons.)Likely means probable, with reference to either a pleasant or unpleasant happening. (It is likely to snow tomorrow.) Locate. Do not use locate to mean settle or move to. Say: We will move to (not locate in) Florida next year. Might of, must of.

Omit the of.

Myself, himself, yourself. These pronouns are to be used as intensives. (The Chairman himself will open the meeting.) Do not use these pronouns when me, him, or you will serve. Say: We shall be happy if Joe and you (not yourself ) join us for lunch at the Plaza. Nice. See Terrific, terrible. Number, amount. See Amount, number. Of, have.

Do not use of for have in structures like could have.

Off of. Omit the of. Say: The book fell off (not off of ) the shelf. Pour, spill. When one pours, he does it deliberately. (He carefully poured the wine into her glass.) When one spills, he does it accidentally. (I carelessly spilled some wine on her dress.) Practical, practicable. Practical means fitted for actual work. Practicable means feasible or possible. Say: My business partner is a practical man. Say: The boss did not consider the plan practicable for this coming year.

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Principal, principle. Principal applies to a chief or the chief part of something. Principle applies to a basic law. Say: Mr. Jones is the principal of the school. Professor White was the principal speaker. Honesty is a good principle to follow. Raise, rise.


Reason is because. Do not use the expression reason is because—it is always incorrect. Say the reason is that. (The reason Jack failed the course is that he didn’t study.) Regardless. See Irregardless. Respectfully, respectively. Respectfully means with respect as in the complimentary close of a letter, respectfully yours. Respectively means that each item will be considered in the order given. Say: This paper is respectfully submitted. Say: The hero, the heroine, and the villain will be played by Albert, Joan, and Harry respectively. Rise, raise.


Said. Avoid the legalistic use of said like said letter, said plan, said program except in legal writing. Should of. Do not use for should have. Sit, set.


Some. Do not use some when you mean somewhat. Say: I’m confused somewhat (not some). Spill, pour.

See Pour, spill.

Suspicion. Do not use suspicion as a verb when you mean suspect. Take, bring. See Bring, take. Teach, learn. See Learn, teach. Terrific, terrible. Avoid “lazy words.” Many people don’t want to take the trouble to use the exact word. They will use words like terrific, swell, great, beautiful, etc., to describe anything and everything that is favorable. And they will use words like terrible, awful, lousy, miserable, etc., for whatever is unfavorable. Use the exact word. Say: We had a delicious (not terrific) meal. Say: We had a boring (not terrible) weekend. This kind, these kind. This kind is correct—as is that kind, these kinds, and those kinds. (My little brother likes this kind of pears.) These kind and those kind are incorrect. Tr y and. Do not say try and. Say try to. (Try to visit me while I am in Florida.) Uninterested. See Disinterested. Wait for, wait on. Wait for means to await; wait on means to serve. Say: I am waiting for (not on) Carter to call me on the telephone. Way, ways.

Do not use ways for way. Say: It is a long way (not ways) to Japan.

Where. Do not use where in place of that in expressions like the following: I see in the newspaper that (not where) a nuclear reactor may be built a mile away from our house. Would of.

Do not use for would have.

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Grammar and Usage Index

Abstract noun, 5f Active voice, 9f–g Adjective, 1d, 10a–s; article, 10d; clause 2b, 10p; comparison, 10g–h; compound, 10e; dangling modifier, 10k; infinitive, 8e, 10l; kinds, 10c; linking verb, 3o; modifier, 10c; or adverb, 11c; participial, 8d; phrase, 2c, 10o; predicate, 4h; pronoun, 5l Adjective pronoun, 5t Adverb, 1e, 11a; clause, 2b, 11i; comparison, 11f; connective, 12b; dropping “1y,” 11e; infinitive, 8e, 11g; kinds, 11b; linking verb, 11d; or adjective, 11c; phrase, 2c, 11h; placement, 11j–l; relative, 12p; with negative verb, 11e Antecedent, 1b; of pronoun, 5p; with or or nor, 5p Appear, 3o Appositive, 5w Article, 10d Be, 3o Begin, 7j Become, 3o Blow, 7j Break, 7j Burst, 7j Case, 5q; nominative, 5r; objective, 5s; possessive, 5v Catch, 7j Choose, 7j Clause 2a; main, 2b; nonrestrictive, 10q; restrictive, 10q; subject, 3j; subordinate, 2b Collective noun, 5d; number, 5p Come, 7j Common noun, 5c Comparative degree, adjectives, 10h–i; adverbs, 11f Comparison, adjectives, 10g; adverbs, 11f; double comparisons, 10j Complement, 3h; adjective, 4h, 4l; direct object, 4h, 4i; indirect object, 4h; noun, 4i–k; phrase, 4k–l; predicate adjective, 4h, 4l; predicate noun, 4h, 4k; pronoun, 4i–k; verb, 4c; verbal, 4k Complex sentence, 3c, 3f Compound adjective, 10e Compound noun, 1a; plural, 5v Compound preposition, 12c Compound sentence, 3c, 3e Compound–complex sentence, 3c, 3g Concrete noun, 5e Condition, 4e, 9d Conjunction, 1g; connective, 12b; 12g–n

Conjunctive adverb, 12k Connective, 12a–n Contrary to fact, 9d Coordinate conjunction, 12i Correlative conjunction, 12j Dangling participle, 10n Declarative sentence, 3b Definite article, 10d Demonstrative pronoun, 5l Dependent clause, 2b Direct address, 5x Direct object, 4h; clause, 4i; noun, 4i; pronoun, 4i; passive voice, 9k Do, 7j Double comparison, 12j Drink, 7j Drive, 7j Ellipsis, 10k Every, 6d Exclamatory sentence, 3b Expletive, 6h Fall, 7j Feel, 3o Find, 7j Fly, 7j Freeze, 7j Future perfect tense, 7h Future tense, 7g Gender, 5o Gerund, 8c; with linking verb, 3o; noun preceding, 5v; perfect form, 8f; phrase, 2c, 8c; present form, 8f Give, 7j Go, 7j Grow, 3o, 7j Had, 9e Hardly, 11e I, 5u Idioms, 12d–e Imperative mood, 4e, 9c Imperative sentence, 3b Indefinite article, 10d Indefinite pronoun, 5k; singular and plural, 6c–d Independent clause, 2b Indicative mood, 4e, 9b; and subjunctive, 9e Indirect object, 4h; noun, 4j; pronoun, 4j; clause, 4j; with passive, 9k

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Infinitive, 2c; adjective, 8e, 10l; adverb, 8e; noun, 8e; perfect, 8h; phrase, 8e; 10 l–n; present, 8h; subject of, 5u; with linking verb, 3o; with that, 8h Interjection, 1h Interrogative pronoun, 5j, 6i Interrogative sentence 3b Intransitive verb, 3n, 3p It, 6h Its, it’s, 5v Know, 7j Lay, 7j Lie, 7j Linking verb, 3p, 3o Look, 3o Main clause, 2b Many, 6c, 6d Misplaced modifier, 10t Modifiers, 10a–s, 11a–l; adjective, 1d, 10c; adverb, 1e, 11a; dangling, 10k, 10n; misplaced, 10t; placement, 10s, 11j; squinting, 10u, 11l Mood, 4e; imperative, 4e, 9c; indicative, 4e, 9b; subjunctive, 4e, 9d; verb, 4e, 9a Negative construction, 11e Nominative absolute, 5x Nominative case, 5r; direct address, 5x; I, 5u; nominative absolute, 5x; we, 5t Nonrestrictive clause, 10q Nor, or, 6e–g Noun, 1a; abstract, 5f; appositive, 5w; case, 5q; clause, 2b; collective, 5a; common, 5c; concrete, 5e; direct object, 4i; gender, 5o; indirect object, 4j; infinitive, 8e; with linking verb, 3n; number, 5p; phrase, 2c; predicate, 4h; with preposition, 1f; proper, 5b; subject, 3i Number, 6a–k; indefinite pronouns, 6c–d; noun and pronouns, 5p; subject-verb agreement, 6a; verb, 4b Objective case, 5s–u Of, 5v Or or nor, 6e–g Ownership, 5v Parenthetical phrase, 6k Participle, 8d, 8g, 101–n; adjective, 8d, 10l; past, 8g; phrase, 2c, 8d, 101–n; perfect, 8g; present, 8g Parts of speech, 1a–i Passive voice, 9h; to form, 9j; with direct and indirect object, 9k; with transitive verb, 9j Past participle, 8d Past perfect tense, 7f Past subjunctive, 9d Past tense, 7e Person, 6 g–k; of pronoun, 5h; relating to verb, 4c Personal pronoun, 5h; object case, 5s Phrases, 2c; gerund, 8c; infinitive, 8e; participial, 8d; subject, 3j

Positive degree, 10h, 11f Possessive case, 5v Possessive pronoun, 5h Predicate adjective, 4h; with linking verb, 11d Predicate noun, 4h Preposition, 1f; connective, 1g, 12b–f; with noun or pronoun, 1f; phrase, 2c Present participle, 8d Present perfect tense, 7d Present tense, 7c Present subjunctive, 9d Principal parts of verb, 7j Progressive form, 7i Pronoun, 1a; appositive, 5w; case, 5q; connective, 12b, 12o; demonstrative, 5l; direct object, 4i; gender, 5o; indefinite, 5k; indirect object, 4j; interrogative, 5j; with linking verb, 3o; number, 5p; person, 5h; personal, 5h; with preposition, 1f; reflexive, 5m; relative, 5i, 12o; subject, 3i Proper noun, 5b Raise, 7j Reflexive pronoun, 5m Relative adverb, 12p Relative pronoun, 5i, 12o Remain, 3o Restrictive clause, 10q Ring, 7j Rise, 7j Run, 7j Scarcely, 11e Seem, 3o Sentence, 3a–p Set, 7j Simple sentence, 3c–d Sit, 7j Smell, 3o Sound, 3o Speak, 7j Squinting modifier, 10u, 11l Steal, 7j Subject, 3a, 3h–j, 6a–k; agreement with verb, 6a; collective noun, 6b; of infinitive, 5u Subjunctive mood, 4e, 9d; and indicative, 9e; past, 9d; present, 9d; were, 9d; would have and had, 9e Subordinate clause, 2b; adjective, 2b, 10p; adverb, 2b; noun, 2b Subordinate conjunction, 12n Superlative degree, 10h–i; 11f Swim, 7j Take, 7j Taste, 3o Tense, 7a–j Their, they’re, 5v

* This Index does not include items listed in Chapter 13 (Correct Usage: Choosing the Right Word). Since these Correct Usage items are in alphabetical order, it will be easy for you to locate any Correct Usage explanation whatsoever.

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There, 6h Throw, 7j To be, 5u Transitive verb, 3m, 3p; 9j Us, 5t Verb, 4a–1; active voice, 4f; with collective noun, 6b; with interrogative pronoun, 6i; with predicate noun, 6j; passive voice, 4f; principal parts, 7j; progressive form, 7i; of sentence, 3a; and subject, 3k Verbal, 3i, 8a–h Voice, 4f, 9f We, 5t

Wear, 7j Were, 9d What, 5i–j Which, 5i–j Who, 5i–j Whom, 5i–j Who’s, 5v Whose, 5v; interrogative pronoun, 5v; possessive pronoun, 10n; relative pronoun, 5j Would have, 9e Write, 7j You, 5t

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PA R T 9

THE SAT WRITING TEST A major feature of SAT, the new Writing test will include a direct writing sample and multiplechoice questions that require recognition of the conventions of standard written English, appropriate diction, and effective and logical expression. The SAT Writing test will include:

• An essay which will provide a direct measure of writing ability; • Essay topics which will not assume any specific subject-matter knowledge; • Revision-in-context passages which will present a context larger than a discrete sentence and therefore permit questions on logic, coherence, and organization;

• Revision-in-context tasks which are similar to common in-class exercises in which students revise their own essays;

• Usage questions which will require students to recognize errors. Sentence-correction questions will require recognition of errors and selection of the correct rephrasing.

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524 • THE SAT WRITING TEST

The SAT Writing Section The SAT Writing section will measure a student’s mastery of developing and expressing ideas effectively. It will include both multiple-choice items and an essay. The multiple-choice component of the writing section will measure the student’s understanding of how to use language in a clear, consistent manner and how to improve a piece of writing through revision and editing. Students will be asked to recognize sentence errors, to choose the best version of a piece of writing, and to improve paragraphs within a writing context. However, they will not be asked to define or to use grammatical terms, and spelling or capitalization will not be tested. For the essay, students will have 25 minutes to write a first draft of an original essay. This will be a direct measure of their ability, under timed conditions, to do the kind of writing required in most college courses—writing that emphasizes precise use of language, logical presentation of ideas, development of a point of view, and clarity of expression. The combination of the multiple-choice items and the essay will provide an assessment of writing that takes into account both the student’s understanding of the conventions of language and his or her ability to develop ideas in a thoughtful, coherent, and cogent essay. The scores for the SAT Writing section will range from 200 to 800. Two subscores will be given for the writing section: a multiple-choice subscore that will range from 20 to 80 and an essay subscore that will range from 2 to 12. Essays not written on the essay assignment will be given a score of zero. The essay component will count toward roughly onethird of the total writing score, and the multiple-choice component will count toward two-thirds of the total writing score.

Content of the Writing Test Multiple-Choice Questions: 35 Minutes, 49 Questions* • Usage—Identifying Sentence Errors: 18 questions • Sentence Correction—Improving Sentences: 25 questions • Revision-in-Context—Improving Paragraphs: 6 questions

Essay (Writing Exercise): 25 Minutes Scoring the Writing Test All essays will be scored holistically. Two readers will independently read each essay and score according to agreed-upon criteria.

Essay Reporting Service Students may request that copies of essays be sent to high schools and/or colleges.

*The PSAT will include items in this multiple-choice writing section.

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THE SAT WRITING TEST • 525

The Essay on the SAT Writing Test

On the SAT, you will be required to write an essay. Here’s an example of the directions to the Essay: SECTION 2

Time—25 minutes 1 Question

ESSAY

Directions: Consider carefully the following excerpt and the assignment below it. Then plan and write an essay that explains your ideas as persuasively as possible. Keep in mind that the support you provide—both reasons and examples—will help make your view convincing to the reader. Please note the essays are considered “first drafts” and are scored holistically. This means readers will award a score according to the overall quality of the essay. They will take into account aspects of writing such as the development of ideas, supporting examples, organization, word choice, and sentence structure.

The principle is this: each failure leads us closer to deeper knowledge, to greater creativity in understanding old data, to new lines of inquiry. Thomas Edison experienced 10,000 failures before he succeeded in perfecting the lightbulb. When a friend of his remarked that 10,000 failures was a lot, Edison replied, “I didn’t fail 10,000 times, I successfully eliminated 10,000 materials and combinations that didn’t work.”

Myles Brand, “Taking the Measure of Your Success” Assignment: What is your view on the idea that it takes failure to achieve success? In an essay, support your position using an example (or examples) from literature, the arts, history, current events, politics, science and technology, or your experience or observation.

WHEN THE SUPERVISOR ANNOUNCES THAT 25 MINUTES HAVE PASSED, YOU MUST STOP WRITING THE ESSAY. DO NOT GO ON TO ANY OTHER SECTION IN THE TEST. YOU MAY MAKE NOTES ON THIS PAGE, BUT YOU MUST WRITE YOUR ESSAY ON THE ANSWER SHEET.

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Here are some more sample Essay topics: Consider carefully the following statement and the assignment below it. Then, plan and write your essay as directed. “Outrageous behavior is instructive. It reveals to us the limits of our tolerance.” Assignment: The quotation implies that those who go beyond accepted standards help us to clarify our own standards. Do you agree or disagree with the quotation? Discuss, supporting your position with examples from current affairs, literature, histor y, or your own experience.

Consider carefully the following quotation and the assignment following it. Then, plan and write your essay as directed. “People seldom stand up for what they truly believe; instead they merely go along with the popular view.” Assignment: Do you agree or disagree with this statement? Write an essay in which you support your opinion with specific examples from histor y, contemporar y affairs, literature, or personal obser vation.

Consider carefully the following statement and the assignment below it. Then, plan and write your essay as directed. “Ever ything has its cost.” Assignment: Choose an example from literature, current affairs, histor y, or from personal obser vation in which a cause, an ideal, or an object had to be paid for at some cost. What was that cost? Was what was gained worth it, or was the cost too high? Give reasons for your position.

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A Few Words About Scoring the Essay. Even with some errors in spelling, punctuation, and grammar, a student can get a top score on the essay. The highly trained high school and college composition teachers who score the essays will follow a rubric that focuses upon content, organization, and language usage and sentence structure. Each essay will be scored independently by two such readers on a 1–6 scale. If the readers’ scores differ by more than two points, the test will be evaluated by a third reader. We know from our experience with the SAT II: Writing test that fewer than 2 percent of all scored essays require a third reader. The rubric for the SAT Writing section will be similar to the one used for the previous SAT II: Writing Test, which follows:

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The SAT Essay Scoring Guide Score of 6

Score of 5

Score of 4

An essay in this category is outstanding, demonstrating clear and consistent mastery, although it may have a few minor errors. A typical essay

An essay in this category is effective, demonstrating reasonably consistent mastery, although it will have occasional errors or lapses in quality. A typical essay

An essay in this category is competent, demonstrating adequate mastery, although it will have lapses in quality. A typical essay

• effectively and insightfully develops a point of view on the issue and demonstrates outstanding critical thinking, using clearly appropriate examples, reasons, and other evidence to support its position

• effectively develops a point of view on the issue and demonstrates strong critical thinking, generally using appropriate examples, reasons, and other evidence to support its position

• develops a point of view on the issue and demonstrates competent critical thinking, using adequate examples, reasons, and other evidence to support its position

• is well organized and clearly focused, demonstrating clear coherence and smooth progression of ideas

• is well organized and focused, demonstrating coherence and progression of ideas

• is generally organized and focused, demonstrating some coherence and progression of ideas

• exhibits skillful use of language, using a varied, accurate, and apt vocabulary

• exhibits facility in the use of language, using appropriate vocabulary

• exhibits adequate but inconsistent facility in the use of language, using generally appropriate vocabulary

• demonstrates meaningful variety in sentence structure

• demonstrates variety in sentence structure

• demonstrates some variety in sentence structure

• is free of most errors in grammar, usage, and mechanics

• is generally free of most errors in grammar, usage, and mechanics

• has some errors in grammar, usage, and mechanics

Score of 3

Score of 2

Score of 1

An essay in this category is inadequate, but demonstrates developing mastery, and is marked by ONE OR MORE of the following weaknesses:

An essay in this category is seriously limited, demonstrating little mastery, and is flawed by ONE OR MORE of the following weaknesses:

An essay in this category is fundamentally lacking, demonstrating very little or no mastery, and is severely flawed by ONE OR MORE of the following weaknesses:

• develops a point of view on the issue, demonstrating some critical thinking, but may do so inconsistently or use inadequate examples, reasons, or other evidence to support its position

• develops a point of view on the issue that is vague or seriously limited, demonstrating weak critical thinking, providing inappropriate or insufficient examples, reasons, or other evidence to support its position

• develops no viable point of view on the issue, or provides little or no evidence to support its position

• is limited in its organization or focus, or may demonstrate some lapses in coherence or progression of ideas

• is poorly organized and/or focused, or demonstrates serious problems with coherence or progression of ideas

• is disorganized or unfocused, resulting in a disjointed or incoherent essay

• displays developing facility in the use of language, but sometimes uses weak vocabulary or inappropriate word choice

• displays very little facility in the use of language, using very limited vocabulary or incorrect word choice

• displays fundamental errors in vocabulary

• lacks variety or demonstrates problems in sentence structure

• demonstrates frequent problems in sentence structure

• demonstrates severe flaws in sentence structure

• contains an accumulation of errors in grammar, usage, and mechanics

• contains errors in grammar, usage, and mechanics so serious that meaning is somewhat obscured

• contains pervasive errors in grammar, usage, or mechanics that persistently interfere with meaning

Essays not written on the essay assignment will receive a score of zero.

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The Writing Sample

Essays with a Total Score of 12

Writing sample essays are read and scored by “readers,” high school and college teachers who have experience with the writing demonstrated by students at the end of high school. They do not expect polished compositions. Two readers score each essay on a 6-point scale, with 6 as the highest score and 1 as the lowest. The total writing sample score is the sum of the two readers’ scores. It is weighted to equal one-third of the total SAT Writing Test score. If the two readers’ scores are more than two points apart, a third reader resolves the discrepancy.

(Each reader gave the essay a score of 6.)

Sample Essays Reproduced below is a topic used on an SAT Writing Test. You will also see the Scoring Guide for Readers of Student Responses to the Writing Subject Test and actual students’ essays. The Scoring Guide, shown on page 528, is used to instruct essay readers. The directions that follow are identical to those in the test. You have twenty-five minutes to write an essay on the topic assigned below. DO NOT WRITE ON ANOTHER TOPIC. AN ESSAY ON ANOTHER TOPIC IS NOT ACCEPTABLE. The essay is assigned to give you an opportunity to show how well you can write. You should, therefore, take care to express your thoughts on the topic clearly and effectively. How well you write is much more important than how much you write, but to cover the topic adequately you will probably need to write more than one paragraph. Be specific. Your essay must be written on the lines provided on your answer sheet. You will receive no other paper on which to write. You will find that you have enough space if you write on every line, avoid wide margins, and keep your handwriting to a reasonable size. It is important to remember that what you write will be read by someone who is not familiar with your handwriting. Try to write or print so that what you are writing is legible to the reader. Consider carefully the following statement. Then plan and write your essay as directed. Nothing requires more discipline than freedom.

Assignment: In an essay, discuss your view of the statement above. Support your view with an example or examples from literature, the arts, history, politics, science and technology, current events, or your experience or observation.

Although essays in this category differ in approach, style, and opinion, and have slight differences in quality, they all demonstrate the clear and consistent competence specified in the scoring guide. These essays are characterized by good organization, good command of the language, pertinent support for the ideas being developed, and an effective presentation. These essays are not perfect, nor are they expected to be, for each is only a first draft written in the twenty minutes allotted. The essay below is representative of essays in this category. The ultimate freedom does not require discipline because to be entirely free, one must have no restrictions created by them or the world around them. But ultimate freedom exists only as a concept and while humans can strive to be free, in reality it can never be achieved. Discipline is therefore inescapable. In William Shakespeare’s King Lear, the theme of madness plays a major role in Lear’s life. Lear’s madness becomes his freedom from the rules around him. In the first scene, Lear gives up his land and therefore, power to his daughters, supposedly freeing himself from obligations in his old age. Yet Lear soon finds that his life and the people in his life are not as he once thought them to be. His daughters Regan and Goneril each display cruelty towards him and place restrictions of Lear. By giving up his power, Lear was in fact giving away his freedom. He can no longer do as he pleases, for example, he must beg each daughter to let him live with them. If discipline is taken to mean restrictions and rules placed upon oneself, then Lear in fact has more as a free man than a powerful man. Lear’s freedom, or rather his lack of power, ends up promoting his madness. This madness removes him from obligations, but at the same time creates a different kind of restriction on him. Lear in his mad state may not have restrictions and discipline in the sence generally thought of, but he does in a new sence. The discipline of madness consumes him. Lear, in both his powerful state and his weakened yet free state has freedom and discipline. And while the concept of ultimate freedom is without discipline, Lear’s freedom in both cases is an example of how imperfect freedom does involve discipline. When Lear had power, he was free to make decisions, but these decisions were disciplined choices. When Lear had madness instead of power, he had freedom to do what he wanted, without concern of the consequences, but he had discipline forced upon him by his situation. Because ultimate freedom cannot be attained, freedom as we see it and refer to daily does involve discipline. Only the unachievable, ultimate freedom does not require discipline.

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Essays in this category demonstrate the reasonably consistent competence described in the scoring guide. They present pertinent examples and a developed argument. These essays, however, do contain lapses that keep them out of the top category. These lapses range from an awkward sentence or two to a failure to maintain a consistent tone. Still, whatever the flaws, they do not detract from the overall impression that the writing is well done.

As the scoring guide describes, essays in this category demonstrate adequate competence with occasional errors and lapses in quality. Although the papers show that the writers have adequate command of the skills needed for good writing, the papers have the kinds of flaws that keep them out of the top ranges.

In society today, as well as histories past, we have seen that “nothing requires more discipline than freedom”. Freedom was a principle that people fought and died for. It was an undisputable right that was sometimes put to the test. However, Adeline Yen Mah and Martin Luther King Jr. prove that nothing isn’t worth fighting for. In “Falling Leaves” by Adeline Yen Mah, we can easily sympathize with her struggle for freedom and rights of passage. Ever since she was a young Chinese girl growing up in a male-dominated world, Adeline had to prove to herself and others that she deserved the praise, affection, and education that her three brothers easily attained. With much determination and introspective spirit, she soon learned the power of her will. By speaking out for her wanting to be rid of her provincial education and moving on to higher learning through attending England’s Universities did she recognize that “nothing requires more discipline than freedom.” In addition to Adeline’s opposition, Martin Luther King Jr. was a prominent figure in America’s history that proved that his efforts were not wasted. He was a firm believer of equal rights for his fellow African American people. Without Martin’s unerring attempts at breaking the barriers, there would not have been such a great uproar to stop the injustices. From time to time, people have felt the restraint and oppression, but Adeline and Martin proved that their voices could not go on unheard. They attacked all obstacles and grew strong enough to realize the importance of their cause. The attainment of freedom have bonded these figures into our nation.

In today’s world almost all people are granted certain freedoms in relation to behavior or emotions. In the United States of America this priviledge is especially prevelant through it’s democratic government and the constitution it provides to protect the people’s rights. Because too much unrestricted freedom can hurt a nation, the freedoms granted to the people must be regulated by each person’s self-discipline. As with most things in life, freedom can be taken for granted if responsibility is not taken for one’s own actions. One major freedom given to most teenagers is the priviledge to go away from home for college. This is a major commitment and responsibility because in many cases a student will be living away from his/her parents for the first time. His/her mother and father are no longer around to hassle the youth about homework, going to sleep, or other decisions. It is a beginning college student’s own discipline or practicality that must aid the teen in making such lifestyle choices. In order to succeed and keep the new freedom of living away from home, the student must prove that he or she is mature enough to handle it. The student must organize his/her time apropriately, take care of himself/ herself, and act like an adult. Many personal freedoms and liberties are granted to people in life. In exchange for these rights, human beings must show they are worthy of receiving them by showing discipline and maturity in their actions and decision. If people were to live carelessly without regard for the preciousness of their freedom, the world would be full of chaos and injustice.

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Important Tips on How to Write the Best Essay Making Your Sentences Effective What Is Style? Many good ideas are lost because they are expressed in a dull, wordy, involved way. We often have difficulty following—we may even ignore—instructions that are hard to read. Yet we find other instructions written in such a clear and simple way that a child could easily follow them. This way of writing—the words we choose and the way we use them—we call style. No two people write exactly alike. Even when writing about the same thing, they probably will say it differently. Some will say it more effectively than others, of course; what they say will be more easily read and understood. But there is seldom any one best way to say something. Rather, there are usually several equally good ways. This flexibility is what makes English such a rich language. Style can’t be taught; each person’s style is like personality—it is unique to him or her. But we can each improve our style. Let us consider how we can improve our writing style by improving our sentences.

How to Write Effective Sentences We speak in sentences; we write in sentences. A single word or phrase sometimes carries a complete thought, but sentences are more often the real units of thought communication. Writing good sentences takes concentration, patience, and practice. It involves much more than just stringing words together, one after another, as they tumble from our minds. If writers aren’t careful, their sentences may not mean to the reader what they want them to; they may mean what they didn’t want them to—or they may mean nothing at all. This section discusses five things writers can do to write better sentences—or improve sentences already written. These are: 1. 2. 3. 4. 5.

Create interest Make your meaning clear Keep your sentences brief Make every word count Vary your sentence patterns Let’s consider interest first.

1. Create Interest We can make our writing more interesting by writing in an informal, conversational style. This style also makes our writing easier to understand and our readers more receptive to our thoughts. Listen to two men meeting in the coffee shop. One tells the other, “Let me know when you need more paper clips.” But how would he have written it? Probably as follows:

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Request this office be notified when your activity’s supply of paper clips, wire, steel gem pattern, large type 1, stock No. 7510-634-6516, falls below 30-day level prescribed in AFR 67-1, Vol. II, Section IV, subject: Office Supplies. Requisition will be submitted as expeditiously as possible to preclude noncompliance with appropriate directives.

Judging from the formal, academic style of much of our writing, we want to impress rather than express. There seems to be something about writing that brings out our biggest words, our most complex sentences, and our most formal style. Obviously this is not effective writing. We wouldn’t dare say it aloud this formally for fear someone would laugh at us, but we will write it.

WRITE TO EXPRESS One of the best ways to make our writing more interesting to the reader and, hence, more effective is to write as we talk. Of course we can’t write exactly as we talk, and we shouldn’t want to. We usually straighten out the sentence structure, make our sentences complete rather than fragmentary or run-on, substitute for obvious slang words, and so on. But we can come close to our conversational style without being folksy or ungrammatical or wordy. This informal style is far more appropriate for the kind of writing we do and for the kind of readers we have than the old formal style. And it certainly makes better reading.

BE DEFINITE, SPECIFIC, AND CONCRETE Another way—and one of the surest—to arouse and hold the interest and attention of readers is to be definite, specific, and concrete.

2. Make Your Meaning Clear You do not need to be a grammarian to recognize a good sentence. After all, the first requirement of grammar is that you focus your reader’s attention on the meaning you wish to convey. If you take care to make your meaning clear, your grammar will usually take care of itself. You can, however, do three things to make your meaning clearer to your reader: (1) emphasize your main ideas, (2) avoid wandering sentences, and (3) avoid ambiguity.

EMPHASIZE THE MAIN IDEAS When we talk we use gestures, voice changes, pauses, smiles, frowns, and so on to emphasize our main ideas. In writing we have to use different methods for emphasis. Some are purely mechanical; others are structural. Mechanical devices include capital letters, underlining or italics, punctuation, and headings. Printers used to capitalize the first letter of a word they wanted to emphasize. We still occasionally capitalize, or use a heavier type to emphasize words, phrases, or whole sentences. Sometimes we underline or italicize words that we want to stand out. Often we label or head main sections or subdivisions, as we have done in this book. This effectively separates main ideas and makes them stand out so that our reader doesn’t have to search for them. But mechanical devices for emphasizing an idea—capitalization, particularly—are often overused. The best way to emphasize an idea is to place it effectively in the sentence. The most emphatic position is at the end of the sentence. The next most emphatic position is at the beginning of the sentence. The place of least importance is anywhere in the middle. Remember, therefore, to put the important clause, phrase, name, or idea at the beginning or at the end of your sentences, and never hide the main idea in a subordinate clause or have it so buried in the middle of the sentence that the reader has to dig it out or miss it altogether. Unemphatic: People drive on the left side instead of the right side in England. Better: Instead of driving on the right side, people in England drive on the left.

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AVOID WANDERING SENTENCES All parts of a sentence should contribute to one clear idea or impression. Long, straggling sentences usually contain a hodgepodge of unrelated ideas. You should either break them up into shorter sentences or put the subordinate thoughts into subordinate form. Look at this sentence: The sergeant, an irritable fellow who had been a truck driver, born and brought up in the corn belt of Iowa, strong as an ox and 6 feet tall, fixed an angry eye on the recruit.

You can see that the main idea is “The sergeant fixed an angry eye on the recruit.” That he was an irritable fellow, strong as an ox, and 6 feet tall adds to the main idea. But the facts that he had been a truck driver and had been born in Iowa add nothing to the main thought, and the sentence is better without them. The sergeant, an irritable fellow who was strong as an ox and 6 feet tall, fixed an angry eye on the recruit.

AVOID AMBIGUITY If a sentence can be misunderstood, it will be misunderstood. A sentence that says that “The truck followed the jeep until its tire blew out” may be perfectly clear to the writer, but it will mean nothing to the reader until the pronoun its is identified.

MAKE SURE THAT YOUR MODIFIERS SAY WHAT YOU MEAN “While eating oats, the farmer took the horse out of the stable.” This sentence provides little more than a laugh until you add to the first part of the sentence a logical subject (“the horse”): “While the horse was eating oats, the farmer took him out of the stable.” Sometimes simple misplacement of modifiers in sentences leads to misunderstanding: “The young lady went to the dance with her boyfriend wearing a low-cut gown.” You can clarify this sentence by simply rearranging it: “Wearing a low-cut gown, the young lady went to the dance with her boyfriend.”

3. Keep Your Sentences Brief Sentences written like 10-word advertisements are hard to read. You cannot get the kind of brevity you want by leaving out the articles (a, an, and the). You can get brevity by dividing complex ideas into bite-size sentences and by avoiding unnecessary words and phrases and needless repetition and elaboration. Here are some suggestions that will help you to write short, straightforward sentences.

USE VERBS THAT WORK The verb—the action word—is the most important word in a sentence. It is the power plant that supplies the energy, vitality, and motion in the sentence. So use strong verbs, verbs that really work in your sentences.

USE THE ACTIVE VOICE Sentences written in the basic subject-verb-object pattern are said to be written in the active voice. In such sentences someone or something does something to the object—there is a forward movement of the idea. In sentences written in the passive voice, the subject merely receives the action—it has something done to it by someone or something, and there is no feeling of forward movement of the idea. The active voice, in general, is preferable to the passive voice because it helps to give writing a sense of energy, vitality, and motion. When we use the passive voice predominantly, our writing doesn’t seem to have much life, the actor in the sentences is not allowed to act, and verbs become

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weak. So don’t rob your writing of its power by using the passive voice when you can use the active voice. Nine out of ten sentences will be both shorter (up to 25 percent shorter) and stronger in the active voice. Let’s compare the two voices: Active:

The pilot flew the aircraft. (Actor) (action) (acted upon)

Passive: The aircraft was flown by the pilot. (Acted upon) (action) (actor)

Now let’s see some typical passive examples: The committee will be appointed by the principal. Reports have been received . . . Provisions will be made by the manager in case of a subway strike. Aren’t these familiar? In most of these we should be emphasizing the actor rather than leaving out or subordinating him or her. See how much more effective those sentences are when they are written in the active voice. The principal will appoint the committee. We have received reports . . . The manager will make provisions in case of a subway strike.

AVOID USING THE PASSIVE VOICE The passive voice always takes more words to say what could be said just as well (and probably better) in the active voice. In the passive voice the subject also becomes less personal and may seem less important, and the motion of the sentence grinds to a halt. There are times, of course, when the passive voice is useful and justified—as when the person or thing doing the action is unknown or unimportant. When we use the lifeless passive voice indiscriminately, we make our writing weak, ineffective, and dull. Remember that the normal English word order is subject-verb-object. There may be occasions in your writing when you feel that the passive voice is preferable. But should such an occasion arise, think twice before you write; the passive voice rarely improves your style. Before using a passive construction, make certain that you have a specific reason. After using it, check to see that your sentence is not misleading.

TAKE A DIRECT APPROACH Closely related to passive voice construction is indirect phrasing. It is requested . . . It is recommended . . . It has been brought to the attention of . . . It is the opinion of . . . Again this is so familiar to us that we don’t even question it. But who requested? Who recommended? Who knows? Who believes? No one knows from reading such sentences! This indirect way of writing, this use of the passive voice and the indirect phrase, is perhaps the most characteristic feature of the formal style of the past. There are many explanations for it. A psychiatrist might say the writer was afraid to take the responsibility for what he or she is writing or merely passing the buck. The writer may unjustifiably believe this style makes him or her anonymous, or makes him or her sound less dogmatic and authoritarian.

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Express your ideas immediately and directly. Unnecessary expressions like it, there is, and there are weaken sentences and delay comprehension. They also tend to place part of the sentence in the passive voice. It is the recommendation of the sales manager that the report be forwarded immediately is more directly expressed as The sales manager recommends that we send the report immediately.

Change Long Modifiers

to Shorter Ones

Mr. Barnes, who is president of the board, will preside.

Mr. Barnes, the board president, will preside.

Vehicles that are defective are . . . They gave us a month for accomplishment of the task.

Defective vehicles are . . . They gave us a month to do the job.

Break Up Long Sentences There is not enough time available for the average executive to do everything that might be done and so it is necessary for him to determine wisely the essentials and do them first, then spend the remaining time on things that are “nice to do.”

The average executive lacks time to do everything that might be done. Consequently, he must decide what is essential and do it first. Then he can spend the remaining time on things that are “nice to do.”

4. Make Every Word Count Don’t cheat your readers. They are looking for ideas—for meaning—when they read your letter, report, or directive. If they have to read several words that have little to do with the real meaning of a sentence or if they have to read a number of sentences to get just a little meaning, you are cheating them. Much of their time and effort is wasted because they aren’t getting full benefit from it. They expected something that you didn’t deliver.

MAKE EACH WORD ADVANCE YOUR THOUGHT Each word in a sentence should advance the thought of that sentence. To leave it out would destroy the meaning you are trying to convey. “Naturally,” you say. “Of course!” But reread the last letter you wrote. Aren’t some of your sentences rather wordy? Couldn’t you have said the same thing in fewer words? And finally, how many times did you use a whole phrase to say what could have been said in one word, or a whole clause for what could have been expressed in a short phrase? In short, try tightening up a sentence like this: The reason that prices rose was that the demand was increasing at the same time that the production was decreasing.

Rewritten: Prices rose because the demand increased while production decreased.

Doesn’t our rewrite say the same thing as the original? Yet we have saved the reader some effort by squeezing the unnecessary words out of a wordy sentence. Now try this one: Wordy: The following statistics serve to give a good idea of the cost of production. Improved: The following statistics give a good idea of the production costs. or These statistics show production costs.

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And this one: Wordy: I have a production supervisor who likes to talk a great deal. Improved: I have a talkative production supervisor.

In all of those rewritten sentences we have saved our reader some time. The same thing has been said in fewer words. Of course you can be too concise. If your writing is too brief or terse, it may “sound” rude and abrupt, and you may lose more than you gain. You need, then, to be politely concise. What you are writing, what you are writing about, and whom you are writing for will help you decide just where to draw the line. However, the general rule, make every word count, still stands. Say what you have to say in as few words as clarity and tact will allow.

CONSOLIDATE IDEAS A second way to save the reader’s effort is to consolidate ideas whenever possible. Pack as much meaning as possible into each sentence without making the sentence structure too complicated. Each sentence is by definition an idea, a unit of thought. Each time the readers read one of these units they should get as much meaning as possible. It takes just about as much effort to read a sentence with a simple thought as it does to read one with a strong idea or with two or three strong ideas. There are several things we can do to pack meaning into a sentence. In general, they all have to do with summarizing, combining, and consolidating ideas. Some people write sentences that are weak and insignificant, both in structure and thought. Ordinarily several such sentences can be summarized and the thought put into one good, mature sentence. For example: We left Wisconsin the next morning. I remember watching three aircraft. They were F-4s. They were flying very low. I felt sure they were going to crash over a half a dozen times. The F-4 is new to me. I hadn’t seen one before.

Rewritten: When we left Wisconsin the next morning, I remember watching three F-4s, a type of aircraft I had never seen before. They were flying so low that over a half dozen times I felt sure they were going to crash.

When summarizing like this, be sure to emphasize the main action. Notice in the next example how we have kept the main action as our verb and made the other actions subordinate by changing them to verbals. Poor:

It was in 1959 that he retired from teaching and he devoted his time to writing his autobiography. (three verbs, one verbal)

Improved: In 1959 he retired from teaching to devote his time to writing his autobiography. (one verb, two verbals)

Here is an example similar to ones we might find in a directive: Poor:

The evaluation forms will be picked up from your respective personnel office. You should have these completed by 1700 hours, 18 May. They will be delivered immediately to the security section.

Notice that in the above instructions all of the actions are to be performed by the reader or “you.” Now let’s put these into one sentence, placing the things to be done in a series and using a single subject.

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Improved: Pick up the evaluation forms from your personnel office; complete and deliver them to the security section by 1700 hours, 18 May. (The subject [you] is understood.)

The same thing can be done with subjects or predicates: Poor:

Horror stories shown on television appear to contribute to juvenile delinquency. Comic books with their horror stories seem to have the same effect. Even the reports of criminal activities which appear in our newspapers seem to contribute to juvenile delinquency.

Improved: Television, comic books, and newspapers seem to contribute to juvenile delinquency by emphasizing stories of horror and crime.

There is one more thing we can do to make our sentences better. We can vary their length and complexity. The following paragraphs suggest ways to do this.

5. Vary Your Sentence Patterns We should, as a general rule, write predominantly short sentences. Similarly, we should keep our sentences simple enough for our readers to understand them easily and quickly. But most people soon get tired of nothing but simple, straightforward sentences. So, give your reader an occasional change of pace. Vary both the length and the construction of your sentences.

VARY SENTENCE LENGTH Some writers use nothing but short, choppy sentences (“The road ended in a wrecked village. The lines were up beyond. There was much artillery around.”) In the hands of a Hemingway, from whom this example is taken, short sentences can give an effect of purity and simplicity; in the hands of a less skillful writer, choppy sentences are usually only monotonous. The other extreme, of course, is just as bad. The writer who always writes heavy sentences of 20 to 30 words soon loses the reader. Some great writers use long sentences effectively, but most writers do not. The readability experts suggest that, for the most effective communication, a sentence should rarely exceed 20 words. Their suggestion is a good rule of thumb, but sentence length should vary. And an occasional long sentence is not hard to read if it is followed by shorter ones. A fair goal for most letter-writers is an average of 21 words per sentence, or less. For longer types of writing, such as regulations and manuals, sentences should average 15 words or less. The sentences in opening paragraphs and in short letters may run a little longer than the average.

VARY SENTENCE CONSTRUCTION Just as important as varied sentence length is variety of construction. Four common sentence categories are simple, compound, complex, and compound-complex. A simple sentence consists of only one main (independent) clause: Rain came down in torrents. Rain and hail started falling. (Simple sentence with compound subject) The storm began and soon grew in intensity. (Simple sentence with compound predicate) A compound sentence has two or more main clauses: Rain started falling, and all work stopped. The storm began; all work stopped. The storm began, the workers found shelter, and all work stopped.

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A complex sentence has one main clause and at least one subordinate (dependent) clause. (Subordinate clauses are underlined in the following sentences.) They were just starting their work when the rain started. Before they had made any progress, the rain started falling. The storm, which grew rapidly in intensity, stopped all work. A compound-complex sentence has two or more main clauses and at least one subordinate clause. (Subordinate clauses are underlined in the following sentences.) Rain started falling, and all work stopped before they had made any progress. Although the workers were eager to finish the job, the storm forced them to stop, and they quickly found shelter. They had made some progress before the storm began, but, when it started, all work stopped. The names of the categories are really not important except to remind you to vary your sentence construction when you write. But remember that sentence variety is not just a mechanical chore to perform after your draft is complete. Good sentence variety comes naturally as the result of proper coordination and subordination when you write. For example: If two or more short sentences have the same subject, combine them into one simple sentence with a compound verb: The men were hot. They were tired, too. They were also angry. The men were hot and tired and angry. If you have two ideas of equal weight or parallel thought, write them as two clauses in a compound sentence. The day was hot and humid. The men had worked hard. The men had worked hard, and the day was hot and humid. The day was hot and humid, but the men had worked hard. If one idea is more important than others, put it in the main clause of a complex sentence: Poor:

The men were tired, and they had worked hard, and the day was hot.

Better: The men were tired because they had worked hard on a hot day. or Although the day was hot and the men were tired, they worked hard.

If the adverbial modifier is the least important part of a complex sentence, put it first and keep the end position for the more important main clause: Instead of: The men finished the job in record time, even though the day was hot and humid and they were tired. Better:

Even though the day was hot and humid and the men were tired, they finished the job in record time.

But be careful about having long, involved subordinate clauses come before the main clause. The reader may get lost or confused before getting to your main point or give up before getting to it. Also beware of letting too many modifying words, phrases, or clauses come between the subject and the verb. This is torture for the reader. The subject and the verb are usually the most important elements of a sentence; keep them close together whenever possible.

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Other Types of Questions on the SAT Writing Test

Following are some directions and samples of some of the other question types on the SAT Writing Test. IDENTIFYING ERRORS

Directions: The following sentences test your knowledge of grammar, usage, diction (choice of words), and idiom. Some sentences are correct. No sentence contains more than one error. You will find that the error, if there is one, is underlined and lettered. Elements of the sentence that are not underlined will not be changed. In choosing answers, follow the requirements of standard written English. If there is an error, select the on e u n d e rlin e d p a rt that must be changed to make the sentence correct and fill in the corresponding oval on your answer sheet. If there is no error, fill in answer oval E. EXAMPLE:

SAMPLE ANSWER

T h e o th e r delegates and h im im m e d ia te ly A B C accepted the resolution drafted by the D neutral states. No e r r o r E

A

C

D

E

Sample Questions with Answers 1.

E ven b efo re he became the youngest player to win A the Wimbledon men’s singles championship, Boris B Becker had sensed that his life would no longer be C D the same. No error. E

2.

If any signer of the Constitution was to return to life A for a day, his opinion of our amendments would be B C D interesting. No error. E

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3.

The dean of the college, together w ith some other A B faculty members, are planning a conference for C the purpose of laying down certain regulations. D No error. E

10.

Psychologists and psychiatrists w illtell us that it is A of utmost importance that a disturbed child receive B C professional attention as soo n as possible. D No error. E

4.

If one lives in Florida one day and in Iceland the A B next, he is certain to feel the change in temperature. C D No error. E

11.

After we were waiting in line for three hours, A B much to our disgust, the tickets had been sold out C when we reached the window. No error. D E

5.

Now that the stress of examinations and interviews A are over, we can all relax for a while. No error. B C D E

12.

6.

The industrial tren mo d is in the direction of re A B C machines and less people. No error. D E

That angry outburst of Fath er’s last night was so A annoying that it resulted in our guests packing up B C and leaving this morning. No error. D E

13.

Sharp advances last week in the wholesale price of A beef is a strong indication of higher meat costs to B C come, but so far retail prices continue favorable. D No error. E

14.

An acquaintance with the memoirs of Elizabeth

7.

8.

The American standard of living is still hig h er A B than most of the other countries of the world. C D No error. E

Barrett Browning and Robert Browning enable us A to appreciate the depth of influence that two people B of talent can have on each other. No error. C D E

A tlast, late in the afternoon, a long line of flags and A B colored umbrellas were seen moving toward the C D gate of the palace. No error. E 15.

9.

Du eto the failure of the air-cooling system, many in A the audience had left the meeting before the principal B C speaker arrived. No error. D E

The supervisor wa s a dvise d to give the assignment A to whomever he believed had a strong sense of B C responsibility, and the courage of his conviction. D No error. E

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16.

If he wo u ld h ave lain quietly as instructed by the A B doctor, he might not have had a second heart C D attack. No error. E

21.

The reason mo st Americans d o n ’t pay much attenA B tion to rising African nationalism is because they C D really do not know modern Africa. No error. E

17.

The founder and, for many years, the guiding spirit A B of the “Kenyon Review” is John Crowe Ransom, who C you must know as an outstanding American critic. D N error. o E

22.

There re main nimosity that s many reasons for the a A B exists between the Arab countries and Israel. C D No error. E

23.

The Federal Aviation Administration ord ered an A emergency inspection of several Pan American B planes on account of a Pan American Boeing 707 C had crashed on Bali, in Indonesia. No error. D E

24.

A gang ofarm ed th ieves , directed by a young A woman, has raided the mansion of a gold-mining B C millionaire near Dublin late last night. No error. D E

25.

I had auvinist pig dream that the women a male ch A B of the world rose up and denounced the women’ s C D liberation movement. No error. E

18.

T ree with the philosophy of h o u g h you may not ag A B Malcolm X, you must admit that he had tremendous C influence over a great many followers. No error. D E

19.

There is no objection to him joining the party A provided he is willing to fit in with the plans of the B C group and is ready and able to do his share of the D work. No error. E

20.

C ere opened by a drum and bugle erem o n ies w A B corps of Chinese children parading up Mott Street C in colorfulful uniforms. No error. D E

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IMPROVING SENTENCES

Directions: The following sentences test correctness and effectiveness of expression. In choosing answers, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, sentence construction, and punctuation. In each of the following sentences, part of the sentence or the entire sentence is underlined. Beneath each sentence you will find five ways of phrasing the underlined part. Choice A repeats the original; the other four are different. Choose the answer that best expresses the meaning of the original sentence. If you think the original is better than any of the alternatives, choose it; otherwise choose one of the others. Your choice should produce the most effective sentence—clear and precise, without awkwardness or ambiguity. EXAMPLE:

SAMPLE ANSWER

Laura Ingalls Wilder published her first book a n d s h e w a s s ix ty-fiv e ye a rs o ld th e n . (A) (B) (C) (D) (E)

A

C

D

E

and she was sixty-five years old then when she was sixty-five being age sixty-five years old upon the reaching of sixty-five years at the time when she was sixty-five

Sample Questions with Answers 26.

S uc h o f hi s n ovel s a s wa s h u m or o u s were success ful. (A) Such of his novels as was humorous were successful. (B) Such of his novels as were humorous were successful. (C) His novels such as were humorous were successful. (D) His novels were successful and humorous. (E) Novels such as his humorous ones were successful.

27. Being that the plane was grounded, we stayed over

until the next morning so that we could get the first flight out. (A) Being that the plane was grounded, we stayed over (B) In view of the fact that the plane was grounded, we stayed over (C) Since the plane was grounded, we stayed over (D) Because the plane was grounded, we stood over (E) On account of the plane being grounded, we stayed over

28.

H en everh asan d h en everw ill keep his word. (A) He never has and he never will (B) He has never yet and never will (C) He has not ever and he will not (D) He never has or will (E) He never has kept and he never will

29.

The teacher feltb ad lyb ecau sesh eh ad sco ld ed th e b r i g h t c h i l d who was restless for want of something to do. (A) felt badly because she had scolded the bright child (B) felt badly why she had scolded the bright child (C) felt bad because she had scolded the bright child (D) felt bad by scolding the bright child (E) had felt badly because she scolded the bright child

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30.

This book does not describe the struggle of the blacks to win their voting rights that I bought. (A) does not describe the struggle of the blacks to win their voting rights that I bought (B) does not describe the black struggle to win their voting rights that I bought (C) does not, although I bought it, describe the struggle of the blacks to win their voting rights (D) which I bought does not describe the struggle to win for blacks their voting rights (E) that I bought does not describe the struggle of the blacks to win their voting rights

31.

Barbara cannot help but think that she will win a college scholarship. (A) (B) (C) (D) (E)

32.

In spite of Tom wanting to study, his sister made him wash the dishes. (A) (B) (C) (D) (E)

33.

Barbara cannot help but think Barbara cannot help but to think Barbara cannot help not to think Barbara can help but think Barbara cannot but help thinking

Tom wanting to study the fact that Tom wanted to study Tom’s need to study Tom’s wanting to study Tom studying

The old sea captain told my wife and me many inter esting yarns about his many voyages. (A) (B) (C) (D) (E)

my wife and me me and my wife my wife and I I and my wife my wife along with me

34.

A great many students from several universities are planning to, if the weather is favorable, attend next Saturday’s mass rally in Washington.

(A) are planning to, if the weather is favorable, attend next Saturday’s mass rally in Washington (B) are planning, if the weather is favorable, to attend next Saturday’s mass rally in Washington (C) are planning to attend, if the weather is favorable, next Saturday’s mass rally in Washington (D) are planning to attend next Saturday’s mass rally in Washington, if the weather is favorable (E) are, if the weather is favorable, planning to attend next Saturday’s mass rally in Washington 35. Jane’s body movements are like those of a dancer. (A) (B) (C) (D) (E)

like those of a dancer the same as a dancer like a dancer a dancer’s like those of a dancer’s

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whether they are modifying the words immediately preceding the construction or the words immediately following the construction. As the sentence initially reads, we don’t know whether much to our disgust modifies after we were waiting in line for three hours or the tickets had been sold out when we reached the window.

Explanatory Answers 1.

Choice E is correct. All underlined parts are correct.

2.

Choice A is correct. “If any signer of the Constitution were to return to life . . .” The verb in the “if clause” of a present contrary-to-fact conditional statement must have a past subjunctive form (were).

3.

Choice C is correct. “The dean of the college . . . is planning . . .” The subject of the sentence (dean) is singular. Therefore, the verb must be singular (is planning).

4.


5.

Choice B is correct. “Now that the stress . . . is over . . .” The subject of the subordinate clause is singular (stress). Accordingly, the verb of the clause must be singular (is—not are). Incidentally, examinations and interviews are not subjects—they are objects of the preposition of.

6.

Choice D is correct. “. . . of more machines and fewer people.” We use fewer for persons and things that may be counted. We use less for bulk or mass.

7.

Choice C or D is correct. “. . . than that of most of the other countries of the world.” We must have parallelism so that the word standard in the main clause of the sentence acts as an antecedent for the pronoun that in the subordinate clause. As the original sentence reads, the American standard of living is still higher than the countries themselves. You could also have said, “The American Standard of living is still higher than most of the other countries’ of the world,” making Choice D also correct.

8.

Choice C is correct. “. . . a long line of flags . . . was seen . . .” The subject of the sentence is singular (line). Therefore, the verb must be singular (was seen).

9.

Choice A is correct. “Because of the failure . . .” Never start a sentence with Due to.

10.


11.

Choice C is correct. “After we were waiting in line for three hours, the tickets had, much to our disgust, been sold out when we reached the window.” Avoid squinting constructions—that is, modifiers that are so placed that the reader cannot tell

12.

Choice B is correct. “. . . resulted in our guests’ packing up . . .” A noun or pronoun immediately preceding a gerund is in the possessive case. Note that the noun guests followed by an apostrophe is possessive.

13.

Choice B is correct. “Sharp advances . . . are . . .” Since the subject of the sentence is plural (advances), the verb must be plural (are).

14.

Choice A is correct. “An acquaintance with the memoirs . . . enables us . . .” Since the subject of the sentence is singular (acquaintance), the verb must be singular (enables).

15.

Choice B is correct. “. . . to whoever . . . had a strong sense . . .” The subject of the subordinate clause is whoever, and it takes a nominative form (whoever—not whomever) since it is a subject. Incidentally, the expression he believed is parenthetical, so it has no grammatical relationship with the rest of the sentence.

16.

Choice A is correct. “If he had lain . . .” The verb in the “if clause” of a past contrary-to-fact conditional statement must take the had lain form—not the would have lain form.

17.

Choice C is correct. “. . . John Crowe Ransom, whom you must know as an outstanding American critic.” The direct object of the subordinate clause—or of any clause or sentence—must be in the objective case and, accordingly, must take the objective form (whom—not who).

18.


19.

Choice A is correct. “There is no objection to his joining . . .” We have here a pronoun that is acting as the subject of the gerund joining. As a subject of the gerund, the pronoun must be in the possessive case (his).

20.

Choice D is correct. “. . . of Chinese children parading in colorful uniforms up Mott Street.” In the original sentence, in colorful uniforms was a misplaced modifier.

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21.

Choice D is correct. “The reason . . . is that . . .” We must say the reason is that—not the reason is because.

22.

Choice A is correct. “There remain many reasons . . .” The word “There” in this sentence is an expletive or introductory adverb. The subject of the sentence (“reasons”) must agree with the verb (“remain”) in number.

23.

24.

Choice C is correct. “. . . because a Pan American Boeing 707 had crashed . . .” The word group on account of has the function of a preposition. We need a subordinate conjunction (because) here in order to introduce the clause. Choice B is correct. “. . . raided the mansion . . .” The past tense (raided)—not the present perfect tense (has raided)—is necessary because the sentence has a specific past time reference (last night).

25.


26.

Choice B is correct. Choice A is incorrect because the plural verb (“were”) is necessary. The reason for the plural verb is that the subject “as” acts as a relative pronoun whose antecedent is the plural noun “novels.” Choice B is correct. Choice C is awkward. Choice D changes the meaning of the original sentence—so does Choice E.

27.

Choice C is correct. Choice A is incorrect—never start a sentence with “being that.” Choice B is too wordy. Choice D is incorrect because we “stayed”— not “stood.” Choice E is incorrect because “on account of” may never be used as a subordinate conjunction.

28.

Choice E is correct. Avoid improper ellipsis. Choices A, B, C, and D are incorrect for this reason. The word “kept” must be included since the second part of the sentence uses another form of the verb (“keep”).

29.

Choice C is correct. Choice A is incorrect because the copulative verb “felt” takes a predicate adjective (“bad”)—not an adverb (“badly”). Choice B is incorrect for the same reason. Moreover, we don’t say “felt bad why.” Choice D is incorrect because the verbal phrase “by scolding” is awkward in this context. Choice E is incorrect because of the use of “badly” and because the past perfect form of the verb (“had felt”) is wrong in this time sequence.

30.

Choice E is correct. Choices A, B, and C are incorrect because the part of the sentence that deals with the buying of the book is in the wrong position. Choice D is incorrect because the meaning of the original sentence has been changed. According to this choice, others besides blacks have been struggling.

31.

Choice A is correct. The other choices are unidiomatic.

32.

Choice D is correct. Choice A is incorrect because the possessive form of the noun (“Tom’s”) must be used to modify the gerund (“wanting”). Choice B is too wordy. Choice C changes the meaning of the original sentence. Choice E is incorrect for the same reason that Choice A is incorrect. Also, Choice E changes the meaning of the original sentence.

33.

Choice A is correct. Choice B is incorrect because “wife” should precede “me.” Choice C is incorrect because the object form “me” (not the nominative form “ I”) should be used as the indirect object. Choice D is incorrect for the reasons given above for Choices B and C. Choice E is too roundabout.

34.

Choice D is correct. Choices A, B, C, and E are incorrect because of the misplacement of the subordinate clause (“if the weather is favorable”).

35.

Choice A is correct. Choices B and C are incorrect because of improper ellipsis. The words “those of” are necessary in these choices. Choice D is incorrect because the “body movements” are not “a dancer’s.” The possessive use of “dancer’s” is incorrect in Choice E.

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Improving Paragraphs Revision-in-Context Passage with Questions

Directions: The following passage is an early draft of an essay. Some parts of the passage need to be rewritten. Read the passage and select the best answers for the questions that follow. Some questions are about par ticular sentences or parts of sentences and ask you to improve sentence structure and word choice. Other questions refer to parts of the essay or the entire essay and ask you to consider organization and development. In making your decisions, follow the conventions of standard written English.

(1) In more and more families, both husbands and wives work nowadays and with this there are new problems that result. (2) One reason there are so many two-career couples is that the cost of living is very high. (3) Another is because women are now more independent. (4) An example of a two-career couple is Mr. and Mrs. Long. (5) Mrs. Long is a university professor. (6) Her husband works for a large corporation as a personnel counselor. (7) They have two children. (8) The Longs believe that the number of two-career couples is likely to increase. (9) However, society generally still expects a married woman to continue to fulfill the traditional roles of companion, housekeeper, mother, hostess. (10) Thus, as the Longs have experienced, conflicts arise in many ways. (11) When career opportunities clash, it is difficult for them to decide which career is more important. (12) There are some basic things that can be done to try to solve a couple’s problems. (13) Partners should discuss issues with each other openly. (14) Keep a realistic estimate on how much can be done. (15) Each partner must set priorities, make choices, and agree to trade-offs. (16) Men and women have to understand each other’s feelings and be aware of this problem before they get involved.

(SENTENCE STRUCTURE) 1.

Which of the following is the best revision of the underlined portion of sentence 1 below? In more and more families, both husbands and wives work nowadays and with this there are new problems that result. (A) nowadays, a situation that is causing new problems (B) nowadays and this is what is causing new problems (C) nowadays and this makes them have new problems as a result (D) nowadays and with it are new problems (E) nowadays, they are having new problems (USAGE)

2.

Which of the following is the best revision of the underlined portion of sentence 3 below? Another is because women are now more independent. (A) (B) (C) (D) (E)

is women which are reason is that women are comes from women being reason is due to the fact that women are is caused by the women’s being

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(SENTENCE STRUCTURE)

(SENTENCE COMBINING) 3.

Which of the following is the best way to combine sentences 5, 6, and 7? (A) Mrs. Long, a university professor, and her husband, a personnel counselor for a large corporation, have two children. (B) As a personnel counselor for a large corporation and as a university professor, Mr. and Mrs. Long have two children. (C) Having two children are Mr. and Mrs. Long, a personnel counselor for a large corporation and a university professor. (D) Mrs. Long is a university professor and her husband is a personnel counselor for a large corporation and they have two children. (E) Mr. and Mrs. Long have two children—he is a personnel counselor for a large corporation and she is a university professor.

5.

In the context of the sentences preceding and following sentence 14, which of the following is the best revision of sentence 14? (A) You should keep a realistic estimate of how much you can do. (B) Estimate realistically how much can be done. (C) Keep estimating realistically about how much can be done. (D) They should be estimating realistically about how much it is possible for them to do. (E) They should estimate realistically how much they can do.

Answer Key: 1. A,

(PASSAGE ORGANIZATION) 4.

In relation to the passage as a whole, which of the following best describes the writer’s intention in the second paragraph? (A) (B) (C) (D)

To summarize contradictory evidence To propose a solution to a problem To provide an example To evaluate opinions set forth in the first paragraph (E) To convince the reader to alter his or her opinion

2. B, 3. A,

4. C, 5. E.

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Sample Test with Answers

1 To enter the perceptual world of whales and dolphins, you would have to change your primary sense from sight to sound. 2 Your brain would process and store sound pictures rather than visual images. 3Individuals and other creatures would be recognized either by the sounds they made or by the echoes they returned from the sounds you made. 4Your sense of neighborhood, of where you are, and whom you are with, would be a sound sense. 5Sound is the primary sense in the life of whales and dolphins. 6Vision is often difficult or impossible in the dark and murky seas. 7Many whales and dolphins navigate and hunt at night or below the zone of illuminated water. 8Vision depends on the presence of light, sounds can be made and used at any time of the day or night, and at all depths. 9Sounds are infinitely variable: loud to soft, high notes to low notes, short silences to long silences, and many other combinations. 10 Sounds can be stopped abruptly in order to listen to a neighbor in the silence. 11They can be finitely directed and pinpointed by the listener. 12And communicating and locating by sound does not require a disruption of daily routines. 13Whales and dolphins can keep in sound contact simply by blowing bubbles as they exhale.

1.

2.

(A) The comma after the word light should be omitted and the word and inserted. (B) A semicolon should be substituted for the comma after light. (C) After the word sounds there should be a comma, then the word however, and then another comma. (D) The sentence should begin with the words for instance. (E) The sentence should begin with the word whereas. 3.

Sentence 11 would be more clear if (A) The words by the speaker were added after the word directed. (B) The sentence began with Sounds rather than They. (C) The word finitely were used again before pinpointed. (D) The words by whales or dolphins were inserted after directed. (E) The word always followed the word can.

If the passage were split into two paragraphs, the second paragraph should begin with the sentence (A) Many whales and dolphins navigate and hunt at night or below the zone of illuminated water. (B) Sounds are infinitely variable (etc.). (C) Sound is the primary sense in the life of whales and dolphins. (D) Your sense of neighborhood, of where you are, and whom you are with, would be a sound sense. (E) Vision is often difficult or impossible in the dark and murky seas.

What should be done with sentence 8?

4.

The last sentence, sentence 13, should be (A) (B) (C) (D)

Omitted left as it is placed before sentence 12 expanded to explain that whales and dolphins are mammals and therefore exhale through lungs (E) changed to read: Whales and dolphins can keep in contact with each other through sound simply by blowing bubbles as they exhale.

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immediately that a comparison is about to be made, and the first part of the sentence (“Whereas vision depends on the presence of light”) is now an incomplete thought which must be followed by a comma and then the rest of the sentence.

Explanatory Answers 1.

2.

Choice C is correct. Choice A is incorrect because the sentence is dealing with the limitations in the use of vision in whales and dolphins, and the subject of vision has already been introduced in the previous sentence, sentence 6. Choice B is incorrect for similar reasons: The subject of sound has just been discussed in the previous sentence, and it is logical that this discussion continue. All the sentences before this address themselves to the reader and explain what changes would have to occur in order for us to perceive the world as whales and dolphins do. Sentence 5 turns the discussion to whales and dolphins themselves and their use of sound. (Notice that sentence 1 says “. . . you would have to change your primary sense . . . ,” and sentence 5 says “Sound is the primary sense in the life of whales and dolphins.”) This is the only logical place to begin a second paragraph. Choice D is incorrect because, as it has been stated, sentences 1 through 4 address the reader and therefore belong in one paragraph. Choice E is wrong because, although it is introducing the subject of vision in whales and dolphins for the first time, it is necessary that it follow directly after sentence 5 in order to show that sound is the primary sense because vision is restricted in the dark and murky seas. Choice E is correct. As it stands, sentence 8 contains two complete thoughts—one about vision and one about sound, separated only by a comma, which is grammatically incorrect. Although Choice A remedies this situation, it does not make clear that a comparison is being made between the uses of vision and hearing. This is also true of Choice B. Choice C makes the comparison clear by the use of the word however, but leaves the two thoughts separated only by a comma, and is therefore wrong. Choice D is wrong for two reasons: The sentence is not really giving an example of something which was stated previously, and therefore the words for instance do not make sense here; furthermore, the words for instance do not make the comparison clear, and so the sentence remains as two separate thoughts with only a comma between them. Choice E remedies the situation completely: The word whereas tells us

3.

Choice A is correct. The sentence as it stands is unclear because it would make it seem that the listener directs as well as pinpoints the sounds, whereas it is the speaker who directs them. Therefore Choice A is correct. There is no need for the sentence to begin with the word sounds; since sentence 10 began with it, the word they in sentence 11 clearly refers to sounds. Therefore Choice B does nothing to improve the sentence. Choice C is incorrect because to pinpoint means to locate precisely or exactly, and therefore it would be redundant to insert the word finitely. Although Choice D improves the sentence by telling us who directs the sounds, Choice A is better because it is the speaker who directs the sounds and the listener who pinpoints them, whether whale or dolphin. Choice E is wrong because it would be assumed by the reader that if sounds can be finitely directed and pinpointed, they would be in most cases; to say always can would be too extreme.

4.

Choice B is correct. Sentence 13 is necessary to show that emitting and listening to sounds do not disrupt the routines of whales and dolphins, stated in sentence 12. To omit the sentence, as Choice A suggests, is incorrect. Choice B is correct; it should be left as it is. Choice C is wrong; sentence 13 explains sentence 12, and therefore needs to follow it, not precede it. Choice D is incorrect because the passage is about the use of sound by whales and dolphins, not about the fact that they are mammals. To go into an explanation of this would be to go into disproportionate detail on this one topic. Choice E is wrong for two reasons: (1) The with each other is understood (one has contact with something; otherwise it is not contact). (2) It also implies that whales keep in contact with dolphins and dolphins with whales, whereas what the author means is that whales and dolphins keep in contact with their own kind. To insert with each other, therefore, makes the sentence quite confusing.

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P A R T 10

FIVE SAT PRACTICE TESTS Five Important Reasons for Taking These Practice Tests

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552 • FIVE SAT PRACTICE TESTS

Each of the 5 Practice SATs in the final part of this book is modeled very closely after the actual SAT. You will find that each of these Practice Tests has a) the same level of difficulty as the actual SAT and b) the same question formats that the actual SAT questions have. Accordingly, taking each of the following tests is like taking the actual SAT. There are five important reasons for taking each of these Practice SATs: 1. To find out in which areas of the SAT you are still weak. 2. To know just where to concentrate your efforts to eliminate these weaknesses. 3. To reinforce the Critical Thinking Skills—19 Math Strategies and 16 Verbal Strategies — that you learned in Part 4 of this book, “Using Critical Thinking Skills to Score High on the SAT.” As we advised you, at the beginning of Part 4, diligent study of these strategies will result in a sharp rise in your SAT Math and Verbal scores. 4. To strengthen your Basic Math skills that might still be a bit rusty. We hope that Part 6, “SAT Math Refresher,” helped you substantially to scrape off some of this rust. 5. To strengthen your grammar and writing skills, look at Part 9, The SAT Writing Test and Part 8, The SAT Grammar and Usage Refresher. These five reasons for taking the 5 Practice Tests in this section of the book tie up closely with a very important educational principle: WE LEARN BY DOING!

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FIVE SAT PRACTICE TESTS • 553

10 Tips for Taking the Practice Tests

1.

Observe the time limits exactly as given.

2.

Allow no interruptions.

3.

Permit no talking by anyone in the “test area.”

4.

Use the Answer Sheets provided at the beginning of each Practice Test. Don’t make extra marks. Two answers for one question constitute an omitted question.

5.

Use scratch paper to figure things out. (On your actual SAT, you are permitted to use the testbook for scratchwork.)

6.

Omit a question when you start “struggling” with it. Go back to that question later if you have time to do so.

7.

Don’t get upset if you can’t answer several of the questions. You can still get a high score on the test. Even if only 40 to 60 percent of the questions you answer are correct, you will get an average or above-average score.

8.

You get the same credit for answering an easy question correctly as you do for answering a tough question correctly.

9.

It is advisable to guess if you are sure that at least one of the answer choices is wrong. If you are not sure whether one or more of the answer choices are wrong, statistically it will not make a difference to your total score if you guess or leave the answer blank.

10. Your SAT score increases by approximately 10 points for every answer you get correct.

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SAT TEST 1 To See How You’d Do on an SAT and What You Should Do to Improve. This SAT Test is very much like the actual SAT. It follows the genuine SAT very closely. Taking this Test is like taking the actual SAT. Following is the purpose of taking this Test: 1. to find out what you are weak in and what you are strong in; 2. to know where to concentrate your efforts in order to be fully prepared for the actual test. Taking this test will prove to be a very valuable TIME SAVER for you. Why waste time studying what you already know? Spend your time profitably by studying what you don’t know. That is what this test will tell you. In this book, we do not waste precious pages. We get right down to the business of helping you to increase your SAT scores. Other SAT preparation books place their emphasis on drill, drill, drill. We do not believe that drill work is of primary importance in preparing for the SAT exam. Drill has its place. In fact, this book contains a great variety of drill material—2,500 SAT-type multiple-choice questions (Critical Reading and Math and Writing), practically all of which have explanatory answers. But drill work must be coordinated with learning Critical Thinking Skills. These skills will help you to think clearly and critically so that you will be able to answer many more SAT questions correctly. After you finish the test, you will come to Part 4 of this book—“Using Critical Thinking Skills to Score High on the SAT,” beginning on page 59. Ready? Start taking the test. It’s just like the real thing.

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SAT PRACTICE TEST 1 • 555

Answer Sheet for Practice Test 1

SECTION 1 Begin your essay on this page. If you need more space, continue on the next page. Do not write outside of the essay box.

Continue on the next page if necessary.

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556 • SAT PRACTICE TEST 1

Continuation of ESSAY Section 1 from previous page. Write below only if you need more space.

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Start with number 1 for each new section. If a section has fewer questions than answer spaces, leave the extra answer spaces blank. Be sure to erase any errors or stray marks completely.

SECTION

2

SECTION

3

1 A 2 A

B

C

D

E

11

A

B

C

D

E

21

A

B

C

D

E

31

A

B

C

D

E

B

C

D

E

12

A

B

C

D

E

22

A

B

C

D

E

32

A

B

C

D

E

3 A 4 A

B

C

D

E

13

A

B

C

D

E

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Use the answer spaces in the grids below for Section 2 or Section 3 only if you are told to do so in your test book.

CAUTION

ONLY ANSWERS ENTERED IN THE CIRCLES IN EACH GRID WILL BE SCORED. YOU WILL NOT RECEIVE CREDIT FOR ANYTHING WRITTEN IN THE BOXES ABOVE THE CIRCLES.

Student-Produced Responses 10

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SECTION

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SECTION

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5 A 6 A

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CAUTION



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SECTION

6

SECTION

7

1 A 2 A

B

C

D

E

11

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B

C

D

E

21

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B

C

D

E

31

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C

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5 A 6 A

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7 A 8 A

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D

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9 A 10 A

B

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D

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20 A

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1 A 2 A

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3 A 4 A

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5 A 6 A

B

C

D

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9 A 10 A

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CAUTION



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. 0

.

13

12

11

.

.

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SECTION

8

SECTION

9

SECTION

10

1 A 2 A

B

C

D

E

11

A

B

C

D

E

21

A

B

C

D

E

31

A

B

C

D

E

B

C

D

E

12

A

B

C

D

E

22

A

B

C

D

E

32

A

B

C

D

E

3 A 4 A

B

C

D

E

13

A

B

C

D

E

23

A

B

C

D

E

33

A

B

C

D

E

B

C

D

E

14

A

B

C

D

E

24

A

B

C

D

E

34

A

B

C

D

E

5 A 6 A

B

C

D

E

15

A

B

C

D

E

25

A

B

C

D

E

35

A

B

C

D

E

B

C

D

E

16

A

B

C

D

E

26

A

B

C

D

E

36

A

B

C

D

E

7 A 8 A

B

C

D

E

17

A

B

C

D

E

27

A

B

C

D

E

37

A

B

C

D

E

B

C

D

E

18

A

B

C

D

E

28

A

B

C

D

E

38

A

B

C

D

E

9 A 10 A

B

C

D

E

19

A

B

C

D

E

29

A

B

C

D

E

39

A

B

C

D

E

B

C

D

E

20 A

B

C

D

E

30

A

B

C

D

E

40

A

B

C

D

E

1 A 2 A

B

C

D

E

11

A

B

C

D

E

21

A

B

C

D

E

31

A

B

C

D

E

B

C

D

E

12

A

B

C

D

E

22

A

B

C

D

E

32

A

B

C

D

E

3 A 4 A

B

C

D

E

13

A

B

C

D

E

23

A

B

C

D

E

33

A

B

C

D

E

B

C

D

E

14

A

B

C

D

E

24

A

B

C

D

E

34

A

B

C

D

E

5 A 6 A

B

C

D

E

15

A

B

C

D

E

25

A

B

C

D

E

35

A

B

C

D

E

B

C

D

E

16

A

B

C

D

E

26

A

B

C

D

E

36

A

B

C

D

E

7 A 8 A

B

C

D

E

17

A

B

C

D

E

27

A

B

C

D

E

37

A

B

C

D

E

B

C

D

E

18

A

B

C

D

E

28

A

B

C

D

E

38

A

B

C

D

E

9 A 10 A

B

C

D

E

19

A

B

C

D

E

29

A

B

C

D

E

39

A

B

C

D

E

B

C

D

E

20 A

B

C

D

E

30

A

B

C

D

E

40

A

B

C

D

E

1 A 2 A

B

C

D

E

11

A

B

C

D

E

21

A

B

C

D

E

31

A

B

C

D

E

B

C

D

E

12

A

B

C

D

E

22

A

B

C

D

E

32

A

B

C

D

E

3 A 4 A

B

C

D

E

13

A

B

C

D

E

23

A

B

C

D

E

33

A

B

C

D

E

B

C

D

E

14

A

B

C

D

E

24

A

B

C

D

E

34

A

B

C

D

E

5 A 6 A

B

C

D

E

15

A

B

C

D

E

25

A

B

C

D

E

35

A

B

C

D

E

B

C

D

E

16

A

B

C

D

E

26

A

B

C

D

E

36

A

B

C

D

E

7 A 8 A

B

C

D

E

17

A

B

C

D

E

27

A

B

C

D

E

37

A

B

C

D

E

B

C

D

E

18

A

B

C

D

E

28

A

B

C

D

E

38

A

B

C

D

E

9 A 10 A

B

C

D

E

19

A

B

C

D

E

29

A

B

C

D

E

39

A

B

C

D

E

B

C

D

E

20 A

B

C

D

E

30

A

B

C

D

E

40

A

B

C

D

E

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SAT PRACTICE TEST 1

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SECTION 1

Time: 25 Minutes—Turn to page 555 of your answer sheet to write your ESSAY.

The purpose of the essay is to have you show how well you can express and develop your ideas. You should develop your point of view, logically and clearly present your ideas, and use language accurately. You should write your essay on the lines provided on your answer sheet. You should not write on any other paper. You will have enough space if you write on every line and if you keep your handwriting to a reasonable size. Make sure that your handwriting is legible to other readers. You will have 25 minutes to write an essay on the assignment below. Do not write on any other topic. If you do so, you will receive a score of 0. Think carefully about the issue presented in the following excerpt and the assignment below.

The well-known proverb ‘Ignorance is bliss’ suggests that people with knowledge of the world’s complexities and its limitations are often unhappy, while their less-knowledgeable counterparts remain contented. But how accurate is this folk wisdom? A recent study showed that well-informed people were more likely to report feelings of well-being. In fact, more knowledge leads people to feel better about themselves and more satisfied with their lives. —adapted from Lee Sigelman, “Is Ignorance Bliss? A Reconsideration of the Folk Wisdom”

Assignment: What is your belief on the notion that more knowledge makes one happier? Support your position by citing an example or examples from history, science and technology, literature, the arts, politics, current events, sports, or your observation or experience. DO NOT WRITE YOUR ESSAY IN YOUR TEST BOOK. You will receive credit only for what you write on your answer sheet. BEGIN WRITING YOUR ESSAY ON PAGE 555 OF THE ANSWER SHEET.

If you finish before time is called, you may check your work on this section only. Do not turn to any other section in the test. 562

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SECTION 2 Time: 25 Minutes—Turn to Section 2 (page 557) of your answer sheet to answer the questions in this section. 20 Questions

Directions: For this section, solve each problem and decide which is the best of the choices given. Fill in the corresponding circle on the answer sheet. You may use any available space for scratchwork.

Notes:

REFERENCE INFORMATION

1. The use of a calculator is permitted. 2. All numbers used are real numbers. 3. Figures that accompany problems in this test are intended to provide information useful in solving the problems. They are drawn as accurately as possible EXCEPT when it is stated in a specific problem that the figure is not drawn to scale. All figures lie in a plane unless otherwise indicated. 4. Unless otherwise specified, the domain of any function f is assumed to be the set of all real numbers x for which f(x) is a real number.

1.

The number of degrees of arc in a circle is 360. The sum of the measures in degrees of the angles of a triangle is 180.

If a and b are positive integers and ab 64, what is the smallest possible value of a b? (A) (B) (C) (D) (E)

2.

Find the value of x x 3 x 5 x 6 if x 1. (A) (B) (C) (D) (E)

65 34 20 16 8

4 2 l 2 4

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563

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564 • SAT PRACTICE TEST 1 – SECTION 2 3. AB

Question 5 refers to the following chart.

BA 66 If 0 A 6 and 0 B 6 in the addition problem above, how many different integer values of A are possible? (A) (B) (C) (D) (E)

4.

Two Three Four Five Six

At 8:00 A.M. the outside temperature was 15°F. At 11:00 A.M. the temperature was 0°F. If the temperature continues to rise at the same uniform rate, what will the temperature be at 5:00 P.M. on the same day? (A) (B) (C) (D) (E)

15°F 5°F 0°F 15°F 30°F

5.

Total Price

1 Box of 3 Box of 6

$12.00 $22.50 $43.40

Which of the following is the closest approximation of the lowest cost per shirt, when a box of shirts is purchased? (A) (B) (C) (D) (E)

6.

Number of Shirts

$7.10 $7.20 $7.30 $7.40 $7.50

If 5x2 15x 0 and x 0, find the value of x. (A) 10 (B) 3 (C) 10 (D) 5 (E) 3


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SAT PRACTICE TEST 1 – SECTION 2 • 565

7.

The chickens on a certain farm consumed 600 pounds of feed in half a year. During that time the total number of eggs laid was 5,000. If the feed cost $1.25 per pound, then the feed cost per egg was (A) (B) (C) (D) (E)

$0.0750 $0.1250 $0.15 $0.25 $0.3333

9.

In the figure above, there are three circles, A, B, and C. The area of A is three times that of B, and the area of B is three times that of C. If the area of B is 1, find the sum of the areas of A, B, and C. (A) (B) (C) (D) (E)

8.

3 31/3 41/3 5 61/3

If X is the set of negative numbers and Y is the set of positive numbers, then the union of X and Y and 0 is the set of (A) (B) (C) (D) (E)

all real numbers all integers all rational numbers all irrational numbers all odd integers

Note: Figure not drawn to scale. 10.

In the figure above, two concentric circles with center P are shown. PQR, a radius of the larger circle, equals 9. PQ, a radius of the smaller circle, equals 4. If a circle L (not shown) is drawn with center at R and Q on its circumference, find the radius of circle L. (A) (B) (C) (D) (E)



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566 • SAT PRACTICE TEST 1 – SECTION 2

y

y=

f(x

)

y=

f(x

)

x


11.

What is the slope of line l in the above figure? (A) 3 1 (B) 3 (C) 0 1 (D) 3 (E) 3

The above graph could represent the equation yx y x y x2 y x, x 0 y 0, x 0 y x, x 0 (E) y x

(A) (B (C) (D)

14.

12.

Given ACB is a straight line segment, and C is the midpoint of AB. If the two segments have the lengths shown above, then

Bus A averages 40 kilometers per gallon of fuel. Bus B averages 50 kilometers per gallon of fuel. If the price of fuel is $3 per gallon, how much less would an 800-kilometer trip cost for Bus B than for Bus A? (A) (B) (C) (D) (E)

$18 $16 $14 $12 $10

(A) a 2b 2 (B) a b 5 2 (C) a b 5 (D) a b (E) a 2b


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15.

If an ant runs randomly through an enclosed circular field of radius 2 feet with an inner circle of 1 foot, what is the probability that the ant will be in the inner circle at any one time? 1 (A) 8 1 (B) 6 1 (C) 4 1 (D) 2 (E) 1

18.

The length and width of a rectangle are 3w and w respectively. The length of the hypotenuse of a right triangle, one of whose acute angles is 30°, is 2w. What is the ratio of the area of the rectangle to that of the triangle?

m||n in the figure above. Find y. (A) (B) (C) (D) (E)

16.

17.

10 20 40 65 175

Given 4 percent of (2a b) is 18 and a is a positive integer. What is the greatest possible value of b? (A) (B) (C) (D) (E)

450 449 448 43 8

(A) (B) (C) (D) (E)

23 : 1 3 :l 3 1 : 1 : 2 3 1:6


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19.

At a certain college, the number of freshmen is 1 three times the number of seniors. If of the 4 1 freshmen and of the seniors attend a football 3 game, what fraction of the total number of freshmen and seniors attends the game?

20.

5 (A) 24 13 (B) 48 17 (C) 48 11 (D) 24 23 (E) 48

At Jones College, there are a total of 100 students. If 30 of the students have cars on campus, and 50 have bicycles, and 20 have both cars and bicycles, then how many students have neither a car nor a bicycle on campus? (A) (B) (C) (D) (E)

80 60 40 20 0

STOP If you finish before time is called, you may check your work on this section only. Do not turn to any other section in the test.

Take a 5 minute break before starting section 3

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SECTION 3 Time: 25 Minutes—Turn to Section 3 (page 557) of your answer sheet to answer the questions in this section. 20 Questions

Directions: For this section, solve each problem and decide which is the best of the choices given. Fill in the corresponding circle on the answer sheet. You may use any available space for scratchwork.

Notes:



1.


If 55,555 y 50,505 find the value of 50,505 – 10y. (A) (B) (C) (D) (E)

2.

5.05 0 5 5.05 50.5

3x (4x 2y) (A) (B) (C) (D) (E)

7x 5xy 12x 6xy 12x2 2y 12x2 6xy 12x2 6x

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5.

7 7 77 10 100 1000 (A) (B) (C) (D) (E)

3.

Exactly how many of the boxes listed in the table above are more than 20 decimeters high? (1 decimeter 100 millimeters) (A) (B) (C) (D) (E)

4.

.0091 .7777 .784 .847 .854

Zero One Two Three Four

If a 3 7, then 2a 14 (A) (B) (C) (D) (E)

6 4 2 4 6

6.

Parallel lines m and n are intersected by line l as shown. Find the value of x y. (A) (B) (C) (D) (E)



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7.

According to the table above, which item has the greatest value when P 12? (A) (B) (C) (D) (E)

8.

1 2 3 4 5

3x If 9, find 6x. 4 (A) 12 (B) 18 (C) 27 (D) 36 (E) 72


In the figure above, each pair of intersecting segme nts is perpendicular with lengths as shown. Findthe length of the dash line segment. (A) (B) (C) (D) (E)

7 63 4 2 46 59

10. For how many two-digit positive numbers will trip-

ling the tens digit give us a two-digit number that is triple the original number? (A) (B) (C) (D) (E)

None One Two Three Four


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572 • SAT PRACTICE TEST 1 – SECTION 3 11. If A is the least positive 5-digit integer with non-

zero digits, none of which is repeated, and B is the greatest of such positive integers, then B A

Given the volume of a cube is 8 cubic meters. Find the distance from any vertex to the center point inside the cube.

(A) (B) (C) (D) (E)

(A) (B) (C) (D) (E)

41,976 66,666 86,420 86,424 89,999

12. At one instant, two meteors are 2,500 kilometers

apart and traveling toward each other in straight paths along the imaginary line joining them. One meteor has a velocity of 300 meters per second while the other travels at 700 meters per second. Assuming that their velocities are constant and that they continue along the same paths, how many seconds elapse from the first instant to the time of their collision? (1 kilometer 1000 meters) (A) (B) (C) (D) (E)

13.

14.

1m

2m 22m 23m 3m

The sum of a number of consecutive positive integers will always be divisible by 2 if the number of integers is a multiple of (A) (B) (C) (D) (E)

6 5 4 3 2

250 500 1,250 2,500 5,000


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15.

Find the circumference of a circle that has the same area as a square that has perimeter 2p.

17.

2 (A) 2 (B) p p p (C) 2 2 (D) p (E) 2

A plane left airport A and has traveled x kilometers per hour for y hours. In terms of x and y, how many 2 kilometers from airport A had the plane traveled y 3 hours ago? xy (A) 6 xy (B) 3 (C) xy 3 xy (D) 2 xy (E) 12

16.

a 1 If , where a is a positive integer, which of the b 4 a2 following is a possible value of ? b 1 I. 4 1 II. 2 III. 1 (A) (B) (C) (D) (E)

None I only I and II only I and III only I, II, and III

18.

The average (arithmetic mean) of k scores is 20. The average of 10 of these scores is 15. Find the average of the remaining scores in terms of k. 20k150 (A) 10 20k150 (B) 10 150 20k (C) 10 15 0 2 0 k (D) k 10 20k 150 (E) k 10


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19.

A square has an area of R2. An equilateral triangle has a perimeter of E. If r is the perimeter of the square and e is a side of the equilateral triangle, then, in terms of R and E, e r

20.

5 Using the formula C (F32), if the Celsius (C) 9 temperature increased 35°, by how many degrees would the Fahrenheit (F) temperature be increased? 4° (A) 19 9 (B) 31° (C) 51° (D) 63° (E) 82°

ER (A) 7 4R 3E (B) 3 3E 4R (C) 12 12E R (D) 3 E 12R (E) 3


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SECTION 4 Time: 25 Minutes—Turn to Section 4 (page 558) of your answer sheet to answer the questions in this section. 24 Questions Directions: For this section, solve each problem and decide which is the best of the choices given. Fill in the corresponding circle on the answer sheet. You may use any available space for scratchwork. 3.

Each sentence below has one or two blanks, each blank indicating that something has been omitted. Beneath the sentence are five words or sets of words labeled A through E. Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole.

(A) eccentric (B) controversial (C) easygoing (D) unheralded (E) prolific

Example:

4.

Hoping to ——— the dispute, negotiators proposed a compromise that they felt would be ——— to both labor and management.

5.

1.

C

D

(B) acceptable (D) inappropriate

6.

(A) (B) (C) (D) (E)

portrayed . . strengthening attacked . . pacifying glamorized . . launching viewed . . appraising exposed . . condemning

shattering . . planned exorbitant . . instituted impertinent . . discussed reasonable . . introduced intolerable . . discontinued

Though Socrates was ––——– by his students who found truth in his teachings, his philosophy constituted ––——– to the existent government. (A) (B) (C) (D) (E)

The novel Uncle Tom’s Cabin, which effectively ––——– the unfairness toward black people, was a major influence in ––——– the anti-slavery movement.

constant . . evil casual . . realistic ridiculous . . remote argumentative . . hostile incapacitated . . conditioned

Because auto repair places have such ——— rates, many community colleges have ––——– courses in automotive mechanics. (A) (B) (C) (D) (E)

Because the majority of the evening cable TV programs available dealt with violence and sex, the parents decided that the programs were ——— for the children to watch. (A) exclusive (C) instructive (E) unnecessary

2.

B

The articles that he wrote ran the gamut from the serious to the lighthearted, from objective to the ––——–, from the innocuous to the ––——–. (A) (B) (C) (D) (E)

(A) enforce . . useful (B) end . . divisive (C) overcome . . unattractive (D) extend . . satisfactory (E) resolve . . acceptable A

Having written 140 books to date, he may well be considered one of the most ––——– novelists of the century.

accepted . . a benefit denied . . an innovation appraised . . an exception slighted . . a challenge revered . . a threat


575

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7.

The quotation was erroneously ––—— to a British poet. (A) (B) (C) (D) (E)

resolved attributed activated relegated vitiated

8.

Mindful that his hardworking parents ––——– to give him an education, Lopez, now wealthy, contributes ––——– to scholarship funds for the needy. (A) (B) (C) (D) (E)

planned . . needlessly skimped . . profitably squandered . . sparingly struggled . . generously regaled . . regretfully

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Each passage below is followed by questions based on its content. Answer the questions on the basis of what is stated or implied in each passage and in any introductory material that may be provided.

Questions 9–10 are based on the following passage.


Plutarch admired those who could use life for grand purposes and depart from it as grandly, but he would not pass over weaknesses and vices which marred the grandeur. His hero of heroes is Alexander the Great; he admires him 5 above all other men, while his abomination of abominations is bad faith, dishonorable action. Nevertheless he tells with no attempt to extenuate how Alexander promised a safe conduct to a brave Persian army if they surrendered, and then, “even as they were marching away he fell upon 10 them and put them all to the sword,” “a breach of his word,” Plutarch says sadly, “which is a lasting blemish to his achievements.” He adds piteously, “but the only one.” He hated to tell that story.

It is no longer needful to labor Dickens’ power as a portrayer of modern society nor the seriousness of his “criticism of life.” But we are still learning to appreciate his supreme attainment as an artist. Richnesses of poetic 5 imagery, modulations of emotional tone, subtleties of implication, complex unities of structure, intensities of psychological insight, a panoply of achievement, mount up to overwhelming triumph. Though contemporary readers perhaps still feel somewhat queasy about Dickens’ sentiment, 10 his comedy and his drama sweep all before them. Even his elaborate and multistranded plots are now seen as great symphonic compositions driving forward through theme and variation to the resolving chords on which they close.

9. Which of the following conclusions is least justified

11. According to the passage, readers most recently

1

1

by the passage?

have begun to appreciate Dickens’

(A) Plutarch considered Alexander basically a great man. (B) The Persians believed that Alexander was acting in good faith. (C) The Persians withdrew from the battlefield in orderly array. (D) The author is familiar with Plutarch’s writing. (E) The author considers Plutarch unfair to Alexander.

(A) (B) (C) (D) (E)

10. As used in this passage, the word “extenuate” (line

7) means (A) (B) (C) (D) (E)

interpret exaggerate emphasize excuse condemn

feeling for culture criticisms of life rhythms literary references literary craftsmanship

12. According to the passage, the endings of Dickens’

works are most probably characterized by (A) (B) (C) (D) (E)

frequent use of comic relief unexpected developments visually effective symbols a lack of sense of completion dramatic power


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Questions 13–24 are based on the following passage. The passage describes the author’s attitude toward transportation.

5

10

15

20

25

30

35

40

45

50

Many people who are willing to concede that the railroad must be brought back to life are chiefly thinking of bringing this about on the very terms that have robbed us of a balanced transportation network—that is, by treating speed as the only important factor, forgetting reliability, comfort and safety, and seeking some mechanical dodge for increasing the speed and automation of surface vehicles. My desk is littered with such technocratic fantasies, hopefully offered as “solutions.” They range from oldfashioned monorails and jet-propelled hovercraft (now extinct) to a more scientific mode of propulsion at 2,000 miles an hour, from completely automated highway travel in private cars to automated vehicles a Government department is now toying with for “facilitating” urban traffic. What is the function of transportation? What place does locomotion occupy in the whole spectrum of human needs? Perhaps the first step in developing an adequate transportation policy would be to clear our minds of technocratic cant. Those who believe that transportation is the chief end of life should be put in orbit at a safe lunar distance from the earth. The prime purpose of passenger transportation is not to increase the amount of physical movement but to increase the possibilities for human association, cooperation, personal intercourse, and choice. A balanced transportation system, accordingly, calls for a balance of resources and facilities and opportunities in every other part of the economy. Neither speed nor mass demand offers a criterion of social efficiency. Hence such limited technocratic proposals as that for high-speed trains between already overcrowded and overextended urban centers would only add to the present lack of functional balance and purposeful organization viewed in terms of human need. Variety of choices, facilities and destinations, not speed alone, is the mark of an organic transportation system. And, incidentally, this is an important factor of safety when any part of the system breaks down. Even confirmed air travelers appreciate the railroad in foul weather. If we took human needs seriously in recasting the whole transportation system, we should begin with the human body and make the fullest use of pedestrian movement, not only for health but for efficiency in moving large crowds over short distances. The current introduction of shopping malls, free from wheeled traffic, is both a far simpler and far better technical solution than the many costly proposals for introducing moving sidewalks or other rigidly automated modes of locomotion. At every stage we should provide for the right type of locomotion, at the right speed, within the right radius, to meet human needs. Neither maximum speed nor maximum traffic nor maximum distance has by itself any human significance.

55

60

65

70

75

With the over-exploitation of the particular car comes an increased demand for engineering equipment, to roll ever wider carpets of concrete over the bulldozed landscape and to endow the petroleum magnates of some places with fabulous capacities for personal luxury and political corruption. Finally, the purpose of this system, abetted by similar concentration on planes and rockets, is to keep an increasing volume of motorists and tourists in motion, at the highest possible speed, in a sufficiently comatose state not to mind the fact that their distant destination has become the exact counterpart of the very place they have left. The end product everywhere is environmental desolation. If this is the best our technological civilization can do to satisfy genuine human needs and nurture man’s further development, it’s plainly time to close up shop. If indeed we go farther and faster along this route, there is plenty of evidence to show that the shop will close up without our help. Behind our power blackouts, our polluted environments, our transportation breakdowns, our nuclear threats, is a failure of mind. Technocratic anesthesia has put us to sleep. Results that were predictable—and predicted!— three-quarters of a century ago without awakening any response still find us unready to cope with them—or even to admit their existence.

13.

The author criticizes most railroad advocates because their emphasis is primarily on (A) (B) (C) (D) (E)

14.

monetary costs speed traffic flow reliability pollution

The author states that the purpose(s) of transportation is (are) I. to move people from place to place efficiently II. to increase social contact III. to open up opportunities (A) (B) (C) (D) (E)

15.

I only II only III only I and II only I, II, and III

A solution advocated by the author for transporting masses of people over short distances involves (A) (B) (C) (D) (E)

jet-propelled hovercraft automated vehicles conveyor belts moving sidewalks pedestrian malls


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16.

Excessive reliance on the automobile, according to the author, is associated with (A) (B) (C) (D) (E)

17.

18.

(A) (B) (C) (D) (E) 19.

22.

a balanced transportation system shopping malls an expansion of the interstate highway system less emphasis on technological solutions sacrificing speed for comfort

The author predicts that if we continue our present transportation policy

23.

(A) the distance from the center of a train wheel to the circumference (B) the distance of places (C) the latitude in connection with human needs (D) the traffic in connection with travel (E) the time it takes to go from one place to another 20.

speed traffic flow diversity maximizing distance technological needs

It may be inferred that the author is a(n) (A) (B) (C) (D) (E)

24.

far greater use of walking more resources devoted to transportation abandoning the profit system a better legislative policy automated travel

The author believes that the nation has placed too great an emphasis on all of the following except (A) (B) (C) (D) (E)

we will succumb to a technocratic dictatorship our society may die we will attain a balanced transportation system rockets and planes will predominate human needs will be surrendered

The word “radius” in line 49 refers to

According to the article, the fulfillment of human needs will require (A) (B) (C) (D) (E)

the enrichment of the oil industry monopoly power our transportation breakdown inefficiency in transportation a policy of comfort and convenience at all costs

It can be inferred that the author would oppose (A) (B) (C) (D) (E)

21.

highway engineer historian railroad industry spokesperson lawyer oil baron

It is stated in the article that safety in transportation is aided by the existence of (A) remote air-to-ground control for airplanes (B) technological sophistication (C) a variety of transport modes (D) fail-safe systems (E) a combination of surface and subsurface systems

The author believes that “technocratic” thinking is not consistent with (A) (B) (C) (D) (E)

technological advances the labor relations groups faster-moving vehicles human interests the scientific mode



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SECTION 5 Time: 25 Minutes—Turn to Section 5 (page 558) of your answer sheet to answer the questions in this section. 35 Questions Directions: For this section, solve each problem and decide which is the best of the choices given. Fill in the corresponding circle on the answer sheet. 3. Once a person starts taking addictive drugs it is

most likely he will be led to take more. (A) it is most likely he will be led to take more (B) he will probably take them over and over again (C) it is hard to stop him from taking more (D) he is likely to continue taking them (E) he will have a tendency to continue taking them

The following sentences test correctness and effectiveness of expression. Part of each sentence or the entire sentence is underlined; beneath each sentence are five ways of phrasing the underlined material. Choice A repeats the original phrasing; the other four choices are different. If you think the original phrasing produces a better sentence than any of the alternatives, select choice A; if not, select one of the other choices. In making your selection, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, sentence construction, and punctuation. Your selection should result in the most effective sentence—clear and precise, without awkwardness or ambiguity.

4.

EXAMPLE: Laura Ingalls Wilder published her first book and she was sixty-five years old then. (A) and she was sixty-five years old then (B) when she was sixty-five (C) at age sixty-five years old (D) upon the reaching of sixty-five years (E) at the time when she was sixty-five A

B

C

D

5. Having the highest marks in his class, the college

offered him a scholarship. (A) the college offered him a scholarship (B) the college offered a scholarship to him (C) he was offered a scholarship by the college (D) a scholarship was offered him by the college (E) a college scholarship was offered to him

E

6. The government’s failing to keep it’s pledges will

1. At the top of the hill to the left of the tall oak is where

they live. (A) (B) (C) (D) (E)

We have not yet been informed concerning the one who broke the window. (A) concerning the one who broke the window (B) about the identity of the individual who is responsible for breaking the window (C) of the window-breaker (D) as to who broke the window (E) who broke the window

mean disaster. (A) (B) (C) (D) (E)

to the left of the tall oak where the tall oak is to the left of it and the tall oak is to the left left of the tall oak to the tall oak’s left

The government’s failing to keep it’s pledges The governments failing to keep it’s pledges The government’s failing to keep its pledges The government failing to keep it’s pledges The governments failing to keep their pledges

2. Martin pretended to be asleep whenever she came

into the room. (A) (B) (C) (D) (E)

whenever she came at the time she comes although she came since she came by the time she came


580

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SAT PRACTICE TEST 1 – SECTION 5 • 581 7. Her father along with her mother and sister insist

that she stop smoking. (A) (B) (C) (D) (E)

along with her mother and sister insist along with her mother and sister insists along with her mother and sister are insisting along with her mother and sister were insisting as well as her mother and sister insist

10. The senator was neither in favor of or opposed to

the proposed legislation. (A) or opposed to the proposed legislation (B) and was not opposed to the proposed legislation (C) the proposed legislation or opposed to it (D) nor opposed to the proposed legislation (E) the proposed legislation or opposed to the proposed legislation

8. Most gardeners like to cultivate these kind of

flowers in the early spring. (A) (B) (C) (D) (E)

these kind of flowers these kind of flower them kinds of flowers those kind of flower this kind of flowers

11. Glory as well as gain is to be his reward.

(A) Glory as well as gain is to be his reward (B) As his reward, glory as well as gain is to be his (C) He will be rewarded by glory as well as gain (D) Glory also gain are to be his reward (E) First glory, then gain, will be his reward

9. The doctor informs us that my aunt has not and

never will recover from the fall. (A) has not and never will recover (B) has not recovered and never will (C) has not and never would recover (D) has not recovered and never will recover (E) had not and never will recover


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582 • SAT PRACTICE TEST 1 – SECTION 5 16. Bob wanted to finish his homework completely

The following sentences test your ability to recognize grammar and usage errors. Each sentence contains either a single error or no error at all. No sentence contains more than one error. The error, if there is one, is underlined and lettered. If the sentence contains an error, select the one underlined part that must be changed to make the sentence correct. If the sentence is correct, select choice E. In choosing answers, follow the requirements of standard written English. EXAMPLE: The other delegates and him immediately A B C accepted the resolution drafted by D the neutral states. No error. E A

B

C

D

A before his mother had come home from her B C sister’ s house. No error. D E

17. Inflation together with the high interest rates and

soaring oil prices are hurting the nation’ s A B C economy very seriously . No error. D E 18. When one le a v e s his car to be repaired, he

E

A B assumes that the mechanic will repair the car C good. No error. D E

19. Bob could easily have gotten a higher score on 12. The long lines of cars at gasoline stations have

A disappeared like as if there were never an B C energy crisis. No error. D E

A B his college entrance test if he would have read C more in his school career. No error. D E

20. Any modern novelist would be thrilled to have 13. The man told his son to take the car to the

A B service station because it needed gasoline. C D No error. E

14. The man w h o ’ s temper is u n d e r control at

A B all times is likely to think clearly and to accomplish C D more in his business and social relations. No error. E

15. Whether nineteenth century classics should be

A taught in school today has become a matter A B C of controversy for students and teachers alike. D No error. E

A B his stories compared with Dickens. No error. C D E

21. The automobile industry is experimenting with a

A new type of a motor that will consume less B C gasoline and cause much less pollution. No error. D E

22. Sharon planned to pay around a hundred dollars

A fo r a new spring coat but when she saw a B gorgeous coat w h ich so ld for two hundred C dollars, she decided to buy it. No error. D E


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SAT PRACTICE TEST 1 – SECTION 5 • 583 23. Had Lincoln have been alive during World War II,

A he would have regarded the racial situation in B C the armed forces as a throwback to pre-Civil D War days. No error. E

24. Members of the staff of the District Attorney made

A more than $100,000 from a get- rich-quick scheme B in which investors were bilked of about $1-million. C D No error. E

25.

Since oxygen is indispensable to human life, A scientists are exploring the possibility of providing B C oxygen for future inhabitants of space stations. D No error. E

26.

Its my opinion that le arn in g the correct A B pronunciation should precede any attempt to learn C D the correct spelling of a word. No error. E

27. If I would have known more about the person

A B whom I was writing to, I would have written a better C D answer. No error. E

28. If you compare Bill and Joe as far as scholarship

A B goes, you will have to conclude that Bill is, without C any question, the brightest. No error. D E

29. In spite of how very poor Ellen had done in the art

A B C competition, she was far from discouraged. D No error. E


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584 • SAT PRACTICE TEST 1 – SECTION 5 31. In sentence five To make matters worse should be

Directions: The following passage is an early draft of an essay. Some parts of the passage need to be rewritten. Read the passage and select the best answers for the questions that follow. Some questions are about par ticular sentences or parts of sentences and ask you to improve sentence structure or word choice. Other questions ask you to consider organization and development. In choosing answers, follow the requirements of standard written English.

Questions 30–35 refer to the following passage.

(A) (B) (C) (D) (E)

32. The end of sentence six would be

(A) (B) (C) (D) (E)

(A) placed after sentence three (B) omitted (C) placed after sentence eight, with ordered changed to had ordered (D) made into two sentences, the first to stop after countryside (E) joined to sentence five with which was because 34. Sentence seven would be more accurate if

capitulated were changed to crumbled a drop of blood were changed to further battle surrendered without fighting at all were substi tuted for capitulated without a drop of blood (D) having resisted were substituted for a drop of blood (E) because of bloodshed were substituted for without a drop of blood (A) (B) (C)

30. What should be done with sentence three?

(A) Moreover and its surrounding punctuation should be replaced with a comma. (B) Moreover and its surrounding punctuation should be replaced with when. (C) The Persian leader and surrounding commas should be omitted. (D) The words fierce resistance should be changed to bull-headedness. (E) The sentence should be left as it is except for changing the semicolon in front of moreover to a comma.

improved by adding in the least little way best if left as it is clearer if it ended after cats best if it ended after unharmed improved if it said unhurt without harming them

33. Sentence six should be

1

In fact the Egyptians pushed their cult of cat worship to the point of aberration. 2 Their devotion cost them the loss of a city in 500 B.C. when the Persians laid siege to Pelusium, a city near the present location of Port Said. 3All the tactics of the Persian army had been blocked by the fierce resistance of the Egyptians; moreover, Cambyses, the Persian leader, had a brilliant idea. 4When the moment for the attack came, the Egyptians were appalled to see hundreds of panic-stricken cats surging ahead of the Persian army. 5 To make matters worse, each advancing Persian soldier carried a live cat in his arms. 6 He ordered his soldiers to search out and seize the greatest possible number of cats in the surrounding countryside and to keep them unharmed without hurting them. 7 The Egyptian defenders would not risk harming one cat and the city of Pelusium capitulated without a drop of blood. 8Animal worship was prevalent during Egyptian times.

changed to It was made worse by omitted changed to Plus left as it is placed at the end of the sentence

35. Sentence 8 should be

(A) (B) (C) (D) (E)

left where it is. placed right after sentence 1 placed before sentence 1 omitted placed after sentence 5


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SECTION 6 Time: 25 Minutes—Turn to Section 6 (page 559) of your answer sheet to answer the questions in this section. 18 Questions Directions: This section contains two types of questions. You have 25 minutes to complete both types. For questions 1–8, solve each problem and decide which is the best of the choices given. Fill in the corresponding circle on the answer sheet. You may use any available space for scratchwork.

Notes:



1.


If x is an odd integer, which of the following MUST be even? (A) (B) (C) (D) (E)

x 3x 2x 2 x x2 2.

If a rectangle is drawn on the grid above with M N as one of its diagonals, which of the following could be the coordinates of another vertex of the rectangle? (A) (B) (C) (D) (E)

(1,0) (2,0) (3,3) (4,3) (5,2)


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x 0 1 2 3 4 3.

f(x) 3 4 2 5 8

5.

The degree measures of the four angles of a quadrilateral are w, x, y, and z respectively. If w is the average (arithmetic mean) of x, y, and z, then xyz (A) (B) (C) (D) (E)

According to the table above, for what value of x does f(x) x 2?

45° 90° 120° 180° 270°

(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

6.

y

A certain mixture contains carbon, oxygen, hydrogen, and other elements in the percentages shown in the graph below. If the total mixture weighs 24 pounds, which number represents the closest number of pounds of carbon that is contained in the mixture?

x

4.

Which equation could represent the graph above? (A) (B) (C) (D) (E)

y x3 2 y x 3 2x 4 y x2 y x3 x y x3 x2 x 1

(A) (B) (C) (D) (E)

5.2 4.6 2.1 1.2 0.5


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7.

In the figure above, two bicycles are being pedaled in opposite directions around a circular race track of circumference 120 feet. Bicycle A is traveling at 5 feet/second in the counterclockwise direction, and Bicycle B is traveling at 8 feet/second in the clockwise direction. When Bicycle B has completed exactly 600 revolutions, how many complete revolutions will Bicycle A have made? (A) (B) (C) (D) (E)

180 375 475 960 It cannot be determined from the given information.

8.

A square of side x is inscribed inside an equilateral triangle of area x23. If a rectangle with width x has the same area as the shaded region shown in the figure above, what is the length of the rectangle in terms of x? (A) (B) (C) (D) (E)

3x 1 x3 3 x x(3 1) x23 x2


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Directions: For Student-Produced Response questions 9–18, use the grids at the bottom of the answer sheet page on which you have answered questions 1–8. Each of the remaining 10 questions requires you to solve the problem and enter your answer by marking the circles in the special grid, as shown in the examples below. You may use any available space for scratchwork. 7 Answer: ᎏ or 7/12 12

Grid in result.

➝

冦

7

1

/

2

/ .

.

.

.

0

0

0

➝

➝

Fraction line

1

.

1

2

.

/

/

.

2

5

➝



Answer: 2.5

.

Decimal point

.

0

0

1

1

1

1

2

2

2

1

1

2

2

2

3

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

4

4

5

5

5

5

5

5

5

6

6

6

6

6

6

6

7

7

7

7

7

7

7

8

8

8

8

8

8

8

8

9

9

9

9

9

9

9

9

6

/

.

.

0

0

2

0

/

1

1

.

2

.

0

1

/

/

.

0 1

1

2

2

3

3

3

4

4

4

.

.

0

0

1

1

2

2

2

3

3

3

3

4

4


●


●



●


2 Acceptable ways to grid ᎏ ⫽ .6666 … 3

●


●

●

No question has a negative answer. 1 Mixed numbers such as 2 ᎏ must be gridded as 2 2.5 or 5/2. (If

2

1 /

/

2


1 21 interpreted as ᎏ , not 2 ᎏ .) 2 2

9.

1 1 If ᎏᎏ ⬍ x⬍ ᎏᎏ , find one value of x. 4 3

●

2

/

3

.

/ .

1

6 /

6

6

.

/

6 /

6

7

/

.

.

.

.

.

.

.

.

.

0

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

2

2

3

3

3

3

3

3

3

3

2 3

3

3

4

4

4

4

4

4

4

4

4

4

4

4

5

5

5

5

5

5

5

5

5

5

5

5

6

6

6

6

6

10.

6

6

Given 3x ⫹ y ⫽ 17 and x ⫹ 3y ⫽ ⫺1, find the value of 3x ⫹ 3y.


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14.

How many ordered pairs of integers (x,y) satisfy x2 y2 9?

15.

The figure above demonstrates that 5 straight lines can have 10 points of intersection. What is the maximum number of points of intersection of 4 straight lines?

16.

A boy planned to buy some chocolate bars at 50 cents each but instead decided to purchase 30-cent chocolate bars. If he originally had enough money to buy 21 of the 50-cent bars, how many of the less expensive ones did he buy?

17.

Let d be the least integer greater than 96,666 such that four of d’s digits are identical. Find the value of d96,666.

18.

Find 25 percent of 25 percent of 2.


If RST 80°, find u.

12.

There are 22 people on an island. A tram can carry at most 4 people at a time. What is the least number of trips that the tram must make to the mainland to get all the people to the mainland?

13.

Let us define the operation 䉺 as a 䉺 b (a b)2 (a b)2 Find the value of 18 䉺 2.



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SECTION 7 Time: 25 Minutes—Turn to Section 7 (page 559) of your answer sheet to answer the questions in this section. 24 Questions Directions: For each question in this section, select the best answer from among the choices given and fill in the corresponding circle on the answer sheet.

3.


(A) (B) (C) (D) (E)

Example: Hoping to ——— the dispute, negotiators proposed a compromise that they felt would be ——— to both labor and management.

4.


B

C

D

He tried his hardest to maintain his ——— in the face of the threatening mob. (A) (B) (C) (D) (E)

2.

twisted unaffected incapable repaired demolished

The guerrillas were so ——— that the general had to develop various strategies to trap them. (A) (B) (C) (D) (E)

synthesis analogy fraternity umbrage composure

spiral . . indubitably cancellation . . rapidly problem . . improbably abundance . . consequently incidence . . radically

Although the death of his dog had saddened him markedly, his computer designing skills remained completely ———. (A) (B) (C) (D) (E)

5. 1.

Before the inflation ———, one could have had a complete meal in a restaurant for a dollar, including the tip, whereas today a hot dog, coffee, and dessert would ——— add up to two or three times that much.

distant wild unreasonable elusive cruel

The low-cost apartment buildings, new and well managed, are ——— to those accustomed to living in tenements ——— by shady characters. (A) (B) (C) (D) (E)

a boon . . haunted a specter . . inhabited an exodus . . frequented an example . . viewed a surprise . . approached


590

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The passages below are followed by questions based on their content; questions following a pair of related passages may also be based on the relationship between the paired passages. Answer the questions on the basis of what is stated or implied in the passages and in any introductory material that may be provided.

Questions 6–9 are based on the following passage. Passage 1 Classical physics the physics of the macroscopic world (our world which we can see, touch and hear). It is very appealing to the purist in that there are no uncertainties in measurement of physical quantities. When we set up an 5 apparatus to measure something the apparatus does not interfere with the measurement. For example if we want to figure out how fast something is traveling, we can also find out exactly where it is at the time of measurement of its speed. There is certainty in classical physics, the “exact” 10 physics. Thus when a bridge is built, we know exactly what stress the bridge may withstand. When a car is constructed we know what specifications the engine must have to have the car do what we want. 1

Passage 2 Modern physics or physics of the sub-microscopic world (the world of electrons, protons and neutrons) is very perplexing since there seems to be an apparent violation of cause and effect. There exists only a probability and not certainty in measurement of important physical quantities because the measurement device affects the measurement. 20 For example, if we know exactly what position an electron is, we cannot determine its speed. Thus the more we know the value of one physical quantity, the less certain we are of a corresponding physical quantity. To paraphrase Albert Einstein, “the universe does not play dice with nature.” 25 Ironically, modern physics really controls and determines the outcome of the physics of the macroscopic physics (since the macroscopic world is really made up of constituents in the sub-microscopic realm). Thus modern physics is the foundation of all physics since it contains the 30 basic and fundamental elements used to create all physics. 15

6. It can be assumed that Albert Einstein believed that

(A) only classical physics existed in nature. (B) there was certainty in all aspects of physics theories (C) classical physics violates cause and effect (D) speed and position are not the fundamental characteristics of particles (E) when a new car is constructed, in order for it to be most efficient a new physics must be employed.

7.

Modern Physics differs from Classical Physics chiefly in that (A) The measurement device does not affect the measurement in Classical Physics (B) No quantity in modern physics can be determined (C) Modern Physics is not as fundamental as classical physics (D) Classical Physics does not deal primarily with measurement (E) speed is always constant in Classical Physics

8. Which of the following would resolve the seeming

paradox between Modern and Classical Physics? (A) There could be a third type of physics which would incorporate the phenomena of both classical and modern physics. (B) One could consider that physics is either macroscopic or microscopic in nature (C) One would not consider speed and position as a fundamental set of physical quantity (D) Exactness of measurement would not be a requirement in physics (E) One could assume that electrons, protons and neutrons do not exist in nature 9. Which key elements exist in either Classical Physics

or Modern Physics but not in both? (i) existence of cause and effect (ii) probability and not certainty of two quantities (iii) the structure of a bridge (A) (B) (C) (D) (E)

(i) only (ii) only (iii) only (i) and (ii) only (i), (ii), and (iii)


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10.

(A) Where van Gogh’s Art Reached Its Zenith (B) An Unfortunate Mismatch Between Two Great Artists (C) Another Tale of a Genius Unable to Adjust to Society (D) A Prolific Painter Whose Art Will Live On (E) Van Gogh’s Frustration in His Hope to Found a New Artists’ Colony

The following passage tracks the career of the famous artist Vincent van Gogh, and his encounter with another famous artist, Paul Gauguin.

5

10

15

20

25

30

35

40

45

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It was at Arles, the small city in the south of France where he stayed from early in 1888 to the spring of 1889, that Vincent van Gogh had his first real bout with madness. After a quarrel with Paul Gauguin, he cut off part of his own ear. Yet Arles was also the scene of an astonishing burst of creativity. Over the short span of 15 months, van Gogh produced some 200 paintings and more than 100 drawings and watercolors, a record that only Picasso has matched in the modern era. Orchards and wheatfields under the glowing sun, neighbors and townspeople, interiors of the Yellow House where he lived, were all subjects of his frenetic brush. The Arles canvases, alive with color—vermilion, emerald green, Prussian blue and a particularly brilliant yellow—have intensity of feeling that mark the high point of his career, and deeply affected the work of artists to follow, notably the Fauves and the German Expressionists. Van Gogh went to Arles after two years in Paris, where his beloved younger brother Theo, who supported him psychologically and financially for most of his adult life, was an art dealer. In Paris, Vincent had met Gauguin, and other important artists—Lautrec, Degas, Pissarro, and Seurat. Like the last two, he worked in the Neo-Impressionist or Pointillist style—applying color in tiny dots or strokes that “mixed” in the viewer’s eye to create effects of considerable intensity. But he wanted “gayer” colors than Paris provided, the kind of atmosphere evoked by the Japanese prints he so admired. Then, too, the French capital had exhausted him, mentally and physically. He felt that in Arles, not exactly a bustling arts center, he might find serenity, and even establish an artistic tradition. It was van Gogh’s hope of founding a new artists’ colony in the south that made him eager to have Gauguin, whose talent van Gogh readily recognized, join him at Arles. The plan, on Vincent’s part, was for Gauguin to stay in Arles for maybe a year, working and sharing with him the small living quarters and studio he had found for himself and dubbed the Yellow House. At first, the two men got along well. But they did not at all agree on judgments of other artists. Still, Gauguin had an influence on van Gogh. Gauguin began pushing the younger artist to paint from memory rather than actuality. Before the year was up, whether because of Gauguin’s attempts to change van Gogh’s style, or what, the two men had apparently begun to get on each other’s nerves. Gauguin wrote to Theo that he felt he had to return to Paris, citing his and Vincent’s “temperamental incompatibility.” A letter from Vincent to Theo followed, noting that Gauguin was “a little out of sorts with the good town of Arles, and especially with me.” But then, the two apparently made up—but not for long. Gauguin returned to Paris and never saw van Gogh again, although they later had friendly correspondence. Despite any problem with his relationship with Gauguin, van Gogh maintained his enormous creativity and prolific nature in those months in Arles.

Which of the following is the best title for the passage?

11.

According to the passage, which of the following statements is not true? (A) Fauvism is a movement in painting typified by vivid colors. (B) Gauguin was an older man than Theo. (C) Pissarro was a painter associated with the Neo-Impressionist school. (D) Van Gogh’s work began to deteriorate after Gauguin’s departure from Arles. (E) Van Gogh’s behavior was, at times, quite abnormal.

12.

For which of the following reasons did van Gogh decide to leave Paris and go to Arles? I. He sought a different environment for the kind of painting he wished to do. II. He had hopes of forming a new artists’ colony. III. He wanted a more peaceful location where there was less stress. (A) (B) (C) (D) (E)

13.

The word “frenetic” in line 11 most nearly means (A) (B) (C) (D) (E)

14.

II only III only I and II only I and III only I, II, and III

colorful smooth bright rapid frantic

Gauguin’s attitude toward van Gogh is best described in the passage as one of (A) (B) (C) (D) (E)

gentle ridicule unallayed suspicion tolerant acceptance open condescension resentful admiration


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15.

Aside from his quarrel with Gauguin, we may infer that a major contributory reason for van Gogh’s going to the extreme of cutting off part of his ear was his (A) concern about being able to support himself financially (B) inability to get along with Gauguin (C) failure to form an artists’ colony in Arles (D) mental and emotional instability (E) being upset by Gauguin’s attempts to change his style


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Questions 16–24 are based on the following passage. The following passage is excerpted from the essay SelfReliance by the American writer Ralph Waldo Emerson.

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Infancy conforms to nobody: all conform to it, so that one babe commonly makes four or five out of the adults who prattle and play to it. So God has armed youth and puberty and manhood no less with its own piquancy and charm, and made it enviable and gracious and its claims not to be put by, if it will stand by itself. Do not think the youth has no force, because he cannot speak to you and me. Hark! in the next room his voice is sufficiently clear and emphatic. It seems he knows how to speak to his contemporaries. Bashful or bold, then, he will know how to make us seniors very unnecessary. The nonchalance of boys who are sure of a dinner, and would disdain as much as a lord to do or say aught to conciliate one, is the healthy attitude of human nature. A boy is in the parlor what the pit is in the playhouse; independent, irresponsible, looking out from his corner on such people and facts as pass by, he tries and sentences them on their merits, in the swift, summary way of boys, as good, bad, interesting, silly, eloquent, troublesome. He lumbers himself never about consequences, about interests; he gives an independent, genuine verdict. You must court him: he does not court you. But the man is, as it were, clapped into jail by his consciousness. As soon as he has once acted or spoken with eclat, he is a committed person, watched by the sympathy or the hatred of hundreds, whose affections must now enter into his account. There is no Lethe for this. Ah, that he could pass again into his neutrality. These are the voices which we hear in solitude, but they grow faint and inaudible as we enter into the world. Society everywhere is in conspiracy against the manhood of every one of its members. Society is a joint-stock company, in which the members agree, for the better securing of his bread to each shareholder, to surrender the liberty and culture of the eater. The virtue in most request is conformity. Self-reliance is its aversion. It loves not realities and creators, but names and customs. Whoso would be a man must be a nonconformist. He who would gather immortal palms must not be hindered by the name of goodness, but must explore if it be goodness. Nothing is at last sacred but the integrity of your own mind. No law can be sacred to me but that of my nature. Good and bad are but names very readily transferable to that or this; the only right is what is after my constitution, the only wrong what is against it. A man is to carry himself in the presence of all opposition as if every thing were titular and ephemeral but he. I am ashamed to think how easily we capitulate to badges and names, to large societies and dead institutions. Every decent and well-spoken individual affects and sways me more than is right. I ought to go upright and vital, and speak the rude truth in all ways. I shun father and mother and wife and brother, when my genius calls me. I would write on the lintels of the doorpost, Whim. I hope it is somewhat better than whim at last, but we cannot spend the day in explanation. Expect me not to show cause why I seek or why I exclude company. Then, again, do not tell me, as a good man did to-day, of my obligation to put all poor men in good situations. Are they

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my poor? I tell thee, thou foolish philanthropist, that I grudge the dollar, the dime, the cent, I give to such men as do not belong to me and to whom I do not belong. There is a class of persons to whom by all spiritual affinity I am bought and sold; for them I will go to prison, if need be; but your miscellaneous popular charities; the education at college of fools; the building of meeting-houses to the vain end to which many now stand; alms to sots; and the thousandfold Relief Societies;—though I confess with shame I sometimes succumb and give the dollar, it is a wicked dollar which by and by I shall have the manhood to withhold. For nonconformity the world whips you with its displeasure. And therefore a man must know how to estimate a sour face. The by-standers look askance on him in the public street or in the friend’s parlor. If this aversion had its origin in contempt and resistance like his own, he might well go home with a sad countenance; but the sour faces of the multitude, like their sweet faces, have no deep cause, but are put on and off as the wind blows and a newspaper directs. Yet is the discontent of the multitude more formidable than that of the senate and the college. The other terror that scares us from self-trust is our consistency; a reverence for our past act or word, because the eyes of others have no other data for computing our orbit than our past acts, and we are loath to disappoint them. But why should you keep your head over your shoulder? Why drag about this corpse of your memory, lest you contradict somewhat you have stated in this or that public place? Suppose you should contradict yourself; what then? A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines. With consistency a great soul has simply nothing to do. He may as well concern himself with his shadow on the wall. Speak what you think now in hard words; and to-morrow speak what to-morrow thinks in hard words again, though it contradict everything you said to-day.—“Ah, so you shall be sure to be misunderstood.”—Is it so bad, then, to be misunderstood? Pythagoras was misunderstood, and Socrates, and Jesus, and Luther, and Copernicus, and Galileo, and Newton, and every pure and wise spirit that ever took flesh. To be great is to be misunderstood.

16.

The main theme of the selection is best expressed as follows: (A) “A foolish consistency is the hobgoblin of little minds.” (B) “Eternal youth means eternal independence.” (C) “Whoso would be a man must be a nonconformist.” (D) “Colleges are designed to educate fools.” (E) “Infancy conforms to nobody.”


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17.

We are most nonconformist during our period of (A) (B) (C) (D) (E)

18.

21.

infancy puberty youth manhood old age

(A) (B) (C) (D) (E)

According to the author, “To be great is to be misunderstood” means that

22.

(A) (B) (C) (D)

one should never say exactly what one means to be misunderstood is to be great all great men have always been misunderstood a man should not hesitate to change his mind if he sees the need to, even at the risk of being considered inconsistent (E) nice people seldom succeed The refusal of young people to cater to accepted public opinion is, according to the author, (A) (B) (C) (D) (E) 20.

fun-loving and luxury violence and force disrespect and resistance reason and logic spirit and enthusiasm

“I would write on the lintels of the doorpost, Whim.” By this, the author means (A) that one should renounce his immediate family (B) that signposts have an important educational function in our society (C) that an impulsive action may have a subsequent rational explanation (D) that one must never be held responsible for what one says and does (E) that everyone should do foolish things occasionally

characteristic of the rebelliousness of youth a healthy attitude of human nature a manifestation of deep-seated immaturity simply bad manners part of growing up

From the selection, one may infer that the “pit in the playhouse” was (A) a section containing the best seats in the theater (B) favored by independent, outspoken, unselfconscious playgoers (C) an underground theater (D) a generally staid, quiet section of the theater, favored by young people only (E) the actors’ dressing rooms

that the public is anti-culture society is highly organized and structured how society rejects self-reliance that there is no room for solitude in our world the public’s interest in the stock market

The word “eclat” (line 23), as used in this selection, means (A) (B) (C) (D) (E)

23. 19.

“Society is a joint-stock company” etc. is one way in which the author shows

24.

The statement that best sums up the spirit and sense of this selection is (A) “Nothing is at last sacred but the integrity of your own mind.” (B) “With consistency, a great soul has simply nothing to do.” (C) “Do not think the youth has no force, because he cannot speak to you and me.” (D) “The virtue in most request is conformity.” (E) “A man must know how to estimate a sour face.”


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SECTION 8 Time: 20 Minutes—Turn to Section 8 (page 560) of your answer sheet to answer the questions in this section. 16 Questions Directions: For this section, solve each problem and decide which is the best of the choices given. Fill in the corresponding circle on the answer sheet. You may use any available space for scratchwork.

Notes:



1.


Tommy and Bobby like to watch their school's baseball team play. Tommy watched 2/3 of all the games the team played last season. Bobby watched 28 games. If Tommy watched more games than Bobby did last season, which of the following could be the number of games the team played last season? (A) (B) (C) (D) (E)

2.

If 8 people share a winning lottery ticket and divide the cash prize equally, what percent of the prize do 2 of them together receive? (A) (B) (C) (D) (E)

33 36 39 42 45

8% 10 % 20 % 25 % 40 %


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3.

An athlete runs 90 laps in 6 hours. This is the same as how many laps per minute? 1 (A) 15

5.

Which of the following is a graph of y 2x 4?

(A)

y

1 (B) 9 1 (C) 4

x

1 (D) 2 (E) 1 (B)

y

x

(C)

y

x 4.

If x 16, x 3/4 (A) 1/2 (B) 1/4 (C) 1/8

(D)

y

(D) 1/16 (E) 1/32 x

(E)

y

x


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6.

[(3a3b2)3]2 (A) (B) (C) (D) (E)

7.

8.

27a9b6 54a9b6 729a9b6 729a18b12 729a54b16

(A) (B) (C) (D) (E)

3 Given that 10 value p. (A) (B) (C) (D) (E)

5 6 9 12 32

Paul’s average (arithmetic mean) for 3 tests was 85. The average of his scores for the first 2 tests was also 85. What was his score for the third test?

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9.

is equal to p hundredths, find the


The operation ⱓ is defined for all numbers x and y by the following: x ⱓ y 3 xy. For example, 2 ⱓ 7 3 2(7) 17. If y 0 and x is a number such that x ⱓ y 3, then find x. (A) 0 3 (B) y (C) y 3 3 (D) y (E) y 3


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12.

10.

(A) (B) (C) (D) (E)

3w 3z 2x y 2x 2y 2w z

Questions 11–12 refer to the following game. A computer generates numbers. Points are assigned as described in the following table each time any of the four number pairs given appears in a number.

11.

I. 33 is not in the number. II. 34 and 43 are both in the number. III. 43 is in the number.

In the figure above, one side of a triangle has been extended. What is the value of w x y? (A) (B) (C) (D) (E)

If a certain number has 13 points assigned to it, which of the following statements must be true?

13.

I only II only III only I and III only I, II, and III

The ratio of Sue’s age to Bob’s age is 3 to 7. The ratio of Sue’s age to Joe’s is 4 to 9. The ratio of Bob’s age to Joe’s is (A) 28 to 27 (B) 7 to 9 (C) 27 to 28 (D) 10 to 13 (E) 13 to 10

As an example, the number 4,347 is assigned 4 points for “43” and 6 points more for “34,” giving a total of 10 points. Which of the following numbers would be assigned the most points? (A) (B) (C) (D) (E)

934,432 464,457 834,415 437,934 336,283


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600 • SAT PRACTICE TEST 1 – SECTION 8 16. If f(x) ax then

(E) 13 to 10

f(x y) f(x) f(y) f(x y) f(x)f(y) f(x y) f(x) f(y) f(xy) f(x)f(y) x (E) f f(x)/f(y) y (A) (B) (C) (D)

14.

The square in the figure above has two sides tangent to the circle. If the area of the circle is 9a2p 2, find the area of the square in terms of a and p. (A) (B) (C) (D) (E)

15.

12 a2p 2 36 a2p 36 a2p 2 18 a4p 2 9 a 4p 2

Equilateral polygon ABCDEF is inscribed in the circle. If the length of arc BAF is 14p, find the length of the diameter of the circle. (A) (B) (C) (D) (E)

7 14 7p 21 42


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3.


(A) (B) (C) (D) (E)


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1.

C

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D

assumes . . coincide relegates . . deviate accumulates . . simplify insists . . compromise dictates . . vary

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(A) (B) (C) (D) (E)

perceptive negligent resourceful placid exemplary

The ——— in the Bible are both entertaining and instructive. (A) (B) (C) (D) (E)

The typist made no effort to be ——— ; she doublespaced the first and third letter, then single-spaced the second, fourth, and fifth letters.

nubile tranquil obvious cogent imminent

Because of his ——— driving, the other car was forced to turn off the road or be hit. (A) (B) (C) (D) (E)

A sense of fairness ——— that the punishment should fit the crime; yet, in actual practice, judicial decisions ——— greatly for the same type of criminal offense. (A) (B) (C) (D) (E)

2.

B

appearances . . energy mistakes . . success remarks . . connections enemies . . audacity conferences . . patience

Their married life was not ——— since it was fraught with bitter fighting and arguments. (A) (B) (C) (D) (E)


As an outstanding publisher, Alfred Knopf was able to make occasional ———, but his bad judgment was tolerated in view of his tremendous ———.

syllables abatements milestones parables utilities

consistent prompt amicable courteous considerate


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The two passages below are followed by questions based on their content and on the relationship between the two passages. Answer the questions on the basis of what is stated or implied in the passages and in any introductory material that may be provided.

joy, between cruelty and pious tenderness which characterize life in the Middle Ages.

Questions 7–19 are based on the following passages. The following two passages describe different time periods. Passage 1 discusses the medieval time period; Passage 2 describes the present and speculates on the future.

Passage 2

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Passage 1

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To the world when it was half a thousand years younger, the outlines of all things seemed more clearly marked than to us. The contrast between suffering and joy, between adversity and happiness, appeared more striking. All experience had yet to the minds of men the directness and absoluteness of the pleasure and pain of child-life. Every event, every action, was still embodied in expressive and solemn forms, which raised them to the dignity of a ritual. Misfortunes and poverty were more afflicting than at present; it was more difficult to guard against them, and to find solace. Illness and health presented a more striking contrast; the cold and darkness of winter were more real evils. Honors and riches were relished with greater avidity and contrasted more vividly with surrounding misery. We, at the present day, can hardly understand the keenness with which a fur coat, a good fire on the hearth, a soft bed, a glass of wine, were formerly enjoyed. Then, again, all things in life were of a proud or cruel publicity. Lepers sounded their rattles and went about in processions, beggars exhibited their deformity and their misery in churches. Every order and estate, every rank and profession, was distinguished by its costume. The great lords never moved about without a glorious display of arms and liveries, exciting fear and envy. Executions and other public acts of justice, hawking, marriages and funerals, were all announced by cries and processions, songs and music. The lover wore the colors of his lady; companions the emblem of their brotherhood; parties and servants the badges of their lords. Between town and country, too, the contrast was very marked. A medieval town did not lose itself in extensive suburbs of factories and villas; girded by its walls, it stood forth as a compact whole, bristling with innumerable turrets. However tall and threatening the houses of noblemen or merchants might be, in the aspect of the town, the lofty mass of the churches always remained dominant. The contrast between silence and sound, darkness and light, like that between summer and winter, was more strongly marked than it is in our lives. The modern town hardly knows silence or darkness in their purity, nor the effect of a solitary light or a single distant cry. All things presenting themselves to the mind in violent contrasts and impressive forms lent a tone of excitement and passion to everyday life and tended to produce that perpetual oscillation between despair and distracted

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In 1575—over 400 years ago!—the French scholar Louis Le Roy published a learned book in which he voiced despair over the upheavals caused by the social and technological innovations of his time, what we now call the Renaissance. “All is pell-mell, confounded, nothing goes as it should.” We, also, feel that our times are out of joint; we even have reason to believe that our descendants will be worse off than we are. The earth will soon be overcrowded and its resources exhausted. Pollution will ruin the environment, upset the climate, damage human health. The gap in living standards between the rich and the poor will widen and lead the angry, hungry people of the world to acts of desperation including the use of nuclear weapons as blackmail. Such are the inevitable consequences of population and technological growth if present trends continue. But what a big if this is! The future is never a projection of the past. Animals probably have no chance to escape from the tyranny of biological evolution, but human beings are blessed with the freedom of social evolution. For us, trend is not destiny. The escape from existing trends is now facilitated by the fact that societies anticipate future dangers and take preventive steps against expected upheavals. Despite the widespread belief that the world has become too complex for comprehension by the human brain, modern societies have often responded effectively to critical situations. The decrease in birth rates, the partial banning of pesticides, the rethinking of technologies for the production and use of energy are but a few examples illustrating a sudden reversal of trends caused not by political upsets or scientific breakthroughs, but by public awareness of consequences. Even more striking are the situations in which social attitudes concerning future difficulties undergo rapid changes before the problems have come to pass—witness the heated controversies about the ethics of behavior control and of genetic engineering even though there is as yet no proof that effective methods can be developed to manipulate behavior and genes on a population scale. One of the characteristics of our times is thus the rapidity with which steps can be taken to change the orientation of certain trends and even to reverse them. Such changes usually emerge from grassroot movements rather than from official directives.


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7.

Conditions like those described in Passage 1 would most likely have occurred about (A) (B) (C) (D) (E)

8.

55 755 A.D. 1055 A.D. 1455 A.D. 1755 A.D.

The phrase “with greater avidity” in line 13 is best interpreted to mean with greater (A) (B) (C) (D) (E)

9.

A.D.

desire sadness terror silence disappointment

In Passage 1, all of the following are stated or implied about towns in the Middle Ages except (A) (B) (C) (D) (E)

Towns had no suburbs. Towns were always quite noisy. Towns served as places of defense. Towns always had large churches. Merchants lived in the towns.

10. The author’s main purpose in Passage 1 is to

(A) describe the miseries of the period (B) show how life was centered on the town (C) emphasize the uncontrolled and violent course of life at the time (D) point out how the upper classes mistreated the lower classes (E) indicate how religious people were in those days 11. According to Passage 1, people at that time, as

compared with people today, were (A) (B) (C) (D) (E)

worse off better off less intelligent more subdued more sensitive to certain events

12. In the first paragraph of Passage 2, the mood

expressed is one of (A) (B) (C) (D) (E)

blatant despair guarded optimism poignant nostalgia muted pessimism unbridled idealism

13. According to Passage 2, if present trends continue,

which one of the following situations will not occur? (A) New sources of energy from vast coal deposits will be substituted for the soon-to-be-exhausted resources of oil and natural gas. (B) The rich will become richer and the poor will become poorer. (C) An overpopulated earth will be unable to sustain its inhabitants. (D) Nuclear weapons will play a more prominent role in dealings among peoples. (E) The ravages of pollution will render the earth and its atmosphere a menace to mankind. 14. Which of the following is the best illustration of the

meaning of “trend is not destiny” in line 65? (A) Urban agglomerations are in a state of crisis. (B) Human beings are blessed with the freedom of social evolution. (C) The world has become too complex for comprehension by the human brain. (D) Critical processes can overshoot and cause catastrophes. (E) The earth will soon be overcrowded and its resources exhausted. 15. According to Passage 2, evidences of the insight of

the public into the dangers that surround us can be found in all of the following except (A) an increase in the military budget by the president (B) a declining birth rate (C) picketing against expansion of nuclear plants (D) opposition to the use of pesticides (E) public meetings to complain about dumping chemicals 16. The author’s attitude in Passage 2 is one of

(A) (B) (C) (D) (E)

willing resignation definite optimism thinly veiled cynicism carefree abandon angry impatience

17. If there is a continuity in history, which of the fol-

lowing situations in Passage 1 is thought to lead to violence in the future of Passage 2? (A) (B) (C) (D) (E)

the overcrowding of the population the executions in public the contrast between the social classes the contrast between illness and health the contrast between religion and politics

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604 • SAT PRACTICE TEST 1 – SECTION 9 18. One can conclude from reading both passages that

19. From a reading of both passages, one may conclude

the difference between the people in Passage 1 and the people in Passage 2 is that (A) the people in Passage 2 act on their awareness in contrast to the people in Passage 1. (B) the people in Passage 2 are more intense and colorful than the people in Passage 1. (C) there was no controversy between sociology and science in the society in Passage 2 in contrast to the society mentioned in Passage 1. (D) the people in Passage 1 are far more religious. (E) sociological changes were faster and more abrupt with the people of Passage 1.

that (A) people in both passages are equally subservient to authority. (B) the future is a mirror to the past. (C) the topic of biological evolution is of great importance to the scientists of both periods. (D) the evolution of science has created great differences in the social classes. (E) the people in Passage 1 are more involved in ever yday living, whereas the people in Passage 2 are usually seeking change.


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SECTION 10 Time: 10 Minutes—Turn to Section 10 (page 560) of your answer sheet to answer the questions in this section. 14 Questions Directions: For each question in this section, select the best answer from among the choices given and fill in the corresponding circle on the answer sheet. 2. By studying during weekends, her grades improved

surprisingly. (A) By studying during weekends, her grades improved surprisingly. (B) By studying during weekends, she improved her grades surprisingly. (C) She was surprised to find her grades improved after studying during weekends. (D) Her grades, by studying during weekends, improved surprisingly. (E) Surprisingly, by studying during weekends, her grades improved.

The following sentences test correctness and effectiveness of expression. Part of each sentence or the entire sentence is underlined; beneath each sentence are five ways of phrasing the underlined material. Choice A repeats the original phrasing; the other four choices are different. If you think the original phrasing produces a better sentence than any of the alternatives, select choice A; if not, select one of the other choices. In making your selection, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, sentence construction, and punctuation. Your selection should result in the most effective sentence—clear and precise, without awkwardness or ambiguity.

3. The streets here are as dirty as a ny other city,

according to recent research studies. (A) (B) (C) (D) (E)


B

C

D

as dirty as any other city so dirty as any other city dirty like any other city as dirty as those of any other city as those of any city

4. Betty is buxom, with blue eyes, and has a pleasant

manner. (A) with blue eyes, and has a pleasant manner (B) with eyes of blue, and a pleasant manner (C) blue-eyed and pleasant (D) blue eyes as well as pleasant (E) and has blue eyes as well as a pleasant manner

E

5. Further acquaintance with the memoirs of Elizabeth 1. She prefers to write poems which describe the

Barrett Browning and Robert Browning enables us to appreciate the depth of influence that two people of talent can have on one another. (A) of talent can have on one another (B) of talent can exert on one another (C) with talent can have one for the other (D) of talent can have on each other (E) who are talented can have

slums and study the habits of the underprivileged. (A) study the habits of the underprivileged (B) study the underprivileged’s habits (C) studying the habits of the underprivileged (D) to study the habits of the underprivileged (E) she prefers to study the habits of the underprivileged

605

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606 • SAT PRACTICE TEST 1 – SECTION 10 6. If you saw the amount of pancakes he consumed at

breakfast this morning, you would understand why he is so overweight.

(A) If you saw the amount of pancakes he consumed (B) If you would see the amount of pancakes he consumed (C) When you see the amount of pancakes he consumed (D) If you saw the number of pancakes he consumed (E) If you had seen the number of pancakes he consumed 7.

The debutante w ent to the concert w ith her fiancé wearing a sheer blouse. (A) The debutante went to the concert with her fiancé wearing a sheer blouse (B) The debutante went to the concert, wearing a sheer blouse, with her fiancé (C) The debutante, wearing a sheer blouse, went to the concert with her fiancé (D) With her fiancé, wearing a sheer blouse, the debutante went to the concert (E) To the concert, wearing a sheer blouse, went the debutante with her fiancé

10. This test was as hard, if not harder than, the one I

took last week.

(A) (B) (C) (D) (E)

11. We took a plane from JFK Airport which carried few

passengers. (A) We took a plane from JFK Airport which carried few passengers (B) The plane that was taken by us from JFK Airport carries few passengers (C) The plane we took carried few passengers (D) We took a plane which carried few passengers from JFK Airport (E) The plane which we took from JFK Airport carried few passengers

12. I wanted to and would have gone to the play if I

had the money.

(A) (B) (C) (D) (E)

8. Briefly the functions of a military staff are to advise

the commander, transmit his instructions, and the supervision of the execution of his decisions. (A) and the supervision of the execution of his decisions (B) also the supervision of the execution of his decisions (C) and supervising the execution of his decisions (D) and supervise the execution of his decisions (E) and have supervision of the execution of his decisions 9.

The 15- round decision that Frazier w as given over Ali was not popular with all of the boxing fans. (A) The 15-round decision that Frazier was given over Ali (B) Frazier’s 15-round decision over Ali (C) The Frazier 15-round decision over Ali (D) The decision of 15 rounds that Frazier was given over Ali (E) Ali’s 15-round decision that Frazier was given over him

This test was as hard This test was so hard This test was as hard as This test was so hard as This was a test as hard

I wanted to and would have gone Having wanted to, I would have gone I wanted to go and would have gone Although I wanted to go and would have gone I wanted and would have gone

13. Either I’ ll go to the store today or tomorrow

morning. (A) Either I’ll go to the store today or tomorrow morning (B) Either I’ll go to the store today or I’ll go tomorrow morning (C) I’ll go to the store today, or if not today, then tomorrow morning (D) I’ll go to the store either today or tomorrow morning (E) I’ll go either today or tomorrow morning to the store

14. For a while he had a job after school, which caused

his grades to suffer. (A) which caused his grades to suffer (B) and for this reason his grades were suffering (C) and this caused his grades to suffer (D) so his grades suffered as a result of this (E) this was the reason his grades suffered


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Page 607

How Did You Do on This Test?

Step 1.

Go to the Answer Key on pages 608–610.

Step 2. For your “raw score,” calculate it using the directions on pages 611–612. Step 3. Get your “scaled score” for the test by referring to the Raw Score/Scaled Score Conversion Tables on pages 613–615. THERE’S ALWAYS ROOM FOR IMPROVEMENT!

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Page 608


Answer Key for the SAT Practice Test 1 (Math) Section 2

Section 6

Section 3 Correct Answer

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

D B D E B E C A C B B E B D C C C A B C

Correct Answer

Correct Answer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

C D D E D A B E C D C D E C B E B E E D

1 2 3 4 5 6 7 8

Number incorrect

Number incorrect

Student-Produced Response Questions

Number correct

Number incorrect

D E D D E B B D

Number correct

9 Number correct

Section 8

10 11 12 13 14 15 16 17 18

Correct Answer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

E D C C E D C B A A A D A B E B

Number correct

7

/24 or x where .25 x .3333 12 60 6 24 25 6 35 333 1 /8 , .125

Number correct

Number incorrect

Number incorrect

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Page 609


Answer Key for the SAT Practice Test 1 (Critical Reading and Writing) Critical Reading

Section 4


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

D A E D B E B D E D E E B D E A C B B D A C B C


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

E A A B D B A A D A D E E C D C A D B B C E C A

Correct Answer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

E A B B B D D A B C E A A B A B C A E

Number correct

Number incorrect Number correct

Number correct

Number incorrect

Number incorrect

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Writing

Section 1

Essay score

Section 10

Section 5 Correct Answer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

A A D D C C B E D D A B D A E C B D C D B A A E E A A D B B D D A B C

Number correct

Number incorrect

Correct Answer 1 2 3 4 5 6 7 8 9 10 11 12 13 14

D B D C D E C D A C E C D C

Number correct

Number incorrect

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Page 611


Scoring the SAT Practice Test

Get Your Critical Reading Score

Check your responses with the correct answers on the previous pages. Fill in the blanks below and do the calculations to get your math, critical reading, and writing raw scores. Use the table to find your math, critical reading, and writing scaled scores.

How many critical reading questions did you get right?

Get Your Math Score

Section 4: Questions 1–24

__________


__________


__________

Total

__________ (A)

How many math questions did you get right? Section 2: Questions 1–20

__________

How many critical reading questions did you get wrong?


__________



__________


__________

Total

__________ (A)


__________

__________

How many multiple-choice math questions did you get wrong?

Total

__________ (B)

0.25

__________


AB

__________

__________


__________


__________

Total

__________ (B)

Round critical reading raw score to the nearest whole number.

0.25

__________

____________________

AB

__________ Math Raw Score

Round math raw score to the nearest whole number. ____________________ Use the Score Conversion Table to find your math scaled score. ____________________

Critical Reading Raw Score

Use the Score Conversion Table to find your critical reading scaled score. ____________________

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Page 612


Get Your Writing Score How many multiple-choice writing questions did you get right? Section 5: Questions 1–35

__________


__________

Total

__________ (A)

How many multiple-choice writing questions did you get wrong? Section 5: Questions 1–35

__________


__________

Total

__________ (B)

0.25

__________

AB

__________ Writing Raw Score

Round writing raw score to the nearest whole number. ____________________ Use the Score Conversion Table to find your writing multiple-choice scaled score. ____________________ Estimate your essay score using the Essay Scoring Guide. ____________________ Use the SAT Score Conversion Table for Writing Composite to find your writing scaled score. You will need your Writing Raw Score and your Essay Score to use this table. ____________________

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Page 613


SAT Score Conversion Table Raw Score

Critical Reading Scaled Score

67

Writing MultipleChoice Scaled Score*


Raw Score


800

31

510

550

60

66

800

30

510

540

58

65

790

29

500

530

57

64

770

28

490

520

56

63

750

27

490

520

55

62

740

26

480

510

54

61

730

25

480

500

53

60

720

24

470

490

52

59

700

23

460

480

51

58

690

22

460

480

50

57

690

21

450

470

49

56

680

20

440

460

48

55

670

19

440

450

47

54

660

800

18

430

450

46

53

650

790

17

420

440

45

52

650

760

16

420

430

44

51

640

740

15

410

420

44

50

630

720

14

400

410

43

49

620

710

80

13

400

410

42

48

620

700

80

12

390

400

41

47

610

680

80

11

380

390

40

46

600

670

79

10

370

380

39

45

600

660

78

9

360

370

38

44

590

650

76

8

350

360

38

43

590

640

74

7

340

350

37

42

580

630

73

6

330

340

36

41

570

630

71

5

320

330

35

40

570

620

70

4

310

320

34

39

560

610

69

3

300

310

32

38

550

600

67

2

280

290

31

37

550

590

66

1

270

280

30

36

540

580

65

0

250

260

28

35

540

580

64

1

230

240

27

34

530

570

63

2

210

220

25

33

520

560

62

3

200

200

23

32

520

550

61

4

200

200

20

Math Scaled Score

Math Scaled Score

and below

This table is for use only with the test in this book. *The Writing multiple-choice score is reported on a 20–80 scale. Use the SAT Score Conversion Table for Writing Composite for the total writing scaled score.

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Page 614

SAT Score Conversion Table for Writing Composite Writing MultipleChoice Raw Score

Essay Raw Score 0

1

2

3

4

5

6

12

200

200

200

210

240

270

300

11

200

200

200

210

240

270

300

10

200

200

200

210

240

270

300

9

200

200

200

210

240

270

300

8

200

200

200

210

240

270

300

7

200

200

200

210

240

270

300

6

200

200

200

210

240

270

300

5

200

200

200

210

240

270

300

4

200

200

200

230

270

300

330

3

200

210

230

250

290

320

350

2

200

230

250

280

310

340

370

1

210

240

260

290

320

360

380

0

230

260

280

300

340

370

400

1

240

270

290

320

350

380

410

2

250

280

300

330

360

390

420

3

260

290

310

340

370

400

430

4

270

300

320

350

380

410

440

5

280

310

330

360

390

420

450

6

290

320

340

360

400

430

460

7

290

330

340

370

410

440

470

8

300

330

350

380

410

450

470

9

310

340

360

390

420

450

480

10

320

350

370

390

430

460

490

11

320

360

370

400

440

470

500

12

330

360

380

410

440

470

500

13

340

370

390

420

450

480

510

14

350

380

390

420

460

490

520

15

350

380

400

430

460

500

530

16

360

390

410

440

470

500

530

17

370

400

420

440

480

510

540

18

380

410

420

450

490

520

550

19

380

410

430

460

490

530

560

20

390

420

440

470

500

530

560

21

400

430

450

480

510

540

570

22

410

440

460

480

520

550

580

23

420

450

470

490

530

560

590

24

420

460

470

500

540

570

600

25

430

460

480

510

540

580

610

614

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Page 615


Writing MultipleChoice Raw Score

Essay Raw Score 0

1

2

3

4

5

6

26

440

470

490

520

550

590

610

27

450

480

500

530

560

590

620

28

460

490

510

540

570

600

630

29

470

500

520

550

580

610

640

30

480

510

530

560

590

620

650

31

490

520

540

560

600

630

660

32

500

530

550

570

610

640

670

33

510

540

550

580

620

650

680

34

510

550

560

590

630

660

690

35

520

560

570

600

640

670

700

36

530

560

580

610

650

680

710

37

540

570

590

620

660

690

720

38

550

580

600

630

670

700

730

39

560

600

610

640

680

710

740

40

580

610

620

650

690

720

750

41

590

620

640

660

700

730

760

42

600

630

650

680

710

740

770

43

610

640

660

690

720

750

780

44

620

660

670

700

740

770

800

45

640

670

690

720

750

780

800

46

650

690

700

730

770

800

800

47

670

700

720

750

780

800

800

48

680

720

730

760

800

800

800

49

680

720

730

760

800

800

800

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Page 616


CHART FOR SELF-APPRAISAL BASED ON THE PRACTICE TEST YOU HAVE JUST TAKEN The Self-Appraisal Chart below tells you quickly where your SAT strengths and weaknesses lie. Check or circle the appropriate box in accordance with the number of your correct answers for each area of the Practice Test you have just taken.

Writing (Multiplechoice) EXCELLENT GOOD FAIR POOR VERY POOR

42–49 37–41 31–36 20–30 0–19

Sentence Completions 16–19 13–15 9–12 5–8 0–4


Math Questions*

40–48 35–39 26–34 17–25 0–16

44–54 32–43 27–31 16–26 0–15

* Sections 2, 6, 8 only. Note: In our tests, we have chosen to have Section 3 as the experimental section. We have also chosen it to be a math section since we felt that students may need more practice in the math area than in the verbal area. Note that on the actual SAT you will take, the order of the sections can vary and you will not know which one is experimental, so it is wise to answer all sections and not to leave any section out.

SAT-I VERBAL AND MATH SCORE/PERCENTILE CONVERSION TABLE Critical Reading and Writing

Math

SAT scaled Percentile verbal score rank 800 . . . . . . . . . . . . . . . . 99.7 790 . . . . . . . . . . . . . . . . 99.5 740–780 . . . . . . . . . . . . 99 700–730 . . . . . . . . . . . . 97 670–690 . . . . . . . . . . . . 95 640–660 . . . . . . . . . . . . 91 610–630 . . . . . . . . . . . . 85 580–600 . . . . . . . . . . . . 77 550–570 . . . . . . . . . . . . 68 510–540 . . . . . . . . . . . . 57 480–500 . . . . . . . . . . . . 46 440–470 . . . . . . . . . . . . 32 410–430 . . . . . . . . . . . . 21 380–400 . . . . . . . . . . . . 13 340–370 . . . . . . . . . . . . 6 300–330 . . . . . . . . . . . . 2 230–290 . . . . . . . . . . . . 1 200–220 . . . . . . . . . . . . 0–0.5

SAT scaled Percentile math score rank 800 . . . . . . . . . . . . . . . . 99.5 770–790 . . . . . . . . . . . . 99.5 720–760 . . . . . . . . . . . . 99 670–710 . . . . . . . . . . . . 97 640–660 . . . . . . . . . . . . 94 610–630 . . . . . . . . . . . . 89 590–600 . . . . . . . . . . . . 84 560–580 . . . . . . . . . . . . 77 530–550 . . . . . . . . . . . . 68 510–520 . . . . . . . . . . . . 59 480–500 . . . . . . . . . . . . 48 450–470 . . . . . . . . . . . . 37 430–440 . . . . . . . . . . . . 26 390–420 . . . . . . . . . . . . 16 350–380 . . . . . . . . . . . . 8 310–340 . . . . . . . . . . . . 2 210–300 . . . . . . . . . . . . 0.5 200 . . . . . . . . . . . . . . . . 0

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Section 1—Essay The following are guidelines for scoring the essay.

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The SAT Scoring Guide Score of 6

Score of 5

Score of 4



















Score of 3

Score of 2

Score of 1




















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Page 619

Explanatory Answers for Practice Test 1 (continued) Section 2: Math As you read these solutions, you are advised to do two things if you answered the Math question incorrectly: 1. When a specific Strategy is referred to in the solution, study that strategy, which you will find in “Using Critical Thinking Skills in Math Questions” (beginning on page 69). 2. When the solution directs you to the “Math Refresher” (beginning on page 191)—for example, Math Refresher 305—study the 305 Math principle to get a clear idea of the Math operation that was necessary for you to know in order to answer the question correctly.

1.


Substitute 2 into 1 . We get

Given: ab 64 and a and b are positive integers

1 (1)3 (1)5 (1)6 1 1 1 1 2

1

(Use Strategy 7: Use numerics to help find the answer.) If a 64, b 1, then 1 is satisfied and a b 65 If a 32, b 2, then 1 is satisfied and a b 34 If a 16, b 4, then 1 is satisfied and a b 20 If a 8, b 8, then 1 is satisfied and a b 16

(Math Refresher #431 and #429) 3.

2

Given:

3

0A6 0B6

BA6

5

1 2 3

4

(Use Strategy 7: Use numerics to help find the answer.) Conditions 1 , 2 and 4 can be satisfied when: A 1, B 5 A 2, B 4 A 3, B 3 A 4, B 2 A 5, B 1

(Math Refresher 406) Choice B is correct. Given: x x3 x5 x6 x 1

AB BA 66

(Use Strategy 17: Use the given information effectively.) From 3 we see that

4

The only other pairs of values that satisfy 1 are each of the above pairs of values reversed for a and b. Thus 5 , a b 16, is the smallest value of a b.

2.


1 2

Thus, there are five possible values of A. (Math Refresher 431)

619

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Page 620

620 • SAT PRACTICE TEST 1 – SECTION 2 ANSWERS

4.


6.

Given: Temperature at 11:00 A.M. 0°F Temperature at 8:00 A.M. 15°F Let x Temperature at 5:00 P.M. y Temperature rise

1 2 3

Given: 5x2 15x 0 x0 5x(x 3) 0 5x 0 or x 3 0 x 0 or x 3 x3

(Math Refresher 407)

6

Use 4 , 5 and 6 to find temperature rise from 11:00 A.M. to 5:00 P.M. We get

7. Choice C is correct. (Use Strategy 2: Translate

1 words to algebra.) In year, 600 pounds of feed 2 were used at a rate of $1.25 per pound). Thus (600 pounds) ($1.25 per pound) was spent or $750 was spent. Hence,

3 hour s 15°F 6 hou rs y 3y 6 15°F y 30°F

Total cost for feed Feed cost per egg number of eggs

Use 1 , 3 and 7 to find the final temperature. x 0°F 30°F x 30°F

$750 5,000 eggs

(Math Refresher 120) 5.

3

Applying 2 to 3 , we get

5

Subtract the times in 1 and 3 . We get Time change 6 hours

1 2

Factoring 1 , we get

4

(Use Strategy 13: Find unknowns by subtracting.) Subtract 2 from 1 . We get Temperature rise in 3 hours 15°F


(Use Strategy 19: Factor and reduce.) $75 10 500 10 eggs


$25 3 25 20 eggs $3 per egg 20 $0.15 per egg (Math Refresher 200)

From the chart above, we know 6 shirts $43.40

1

8.

(Use Strategy 13: Find unknowns by division.) Dividing 1 by 6, we get 6 shirts $43.40 6 6 1 shirt $7.233 Cost per shirt $7.20 (Math Refresher 406)

Choice A is correct. The union of X and Y and 0 is the set of all the elements of X and Y and 0. The elements of all negative, 0, and positive numbers is the set of all real numbers. (Math Refresher 802)

9.

Choice C is correct. (Use Strategy 2: Translate from words to algebra.) Given: Area B 1 Area A 3(Area B) Area B 3(Area C)

1 2 3

Substitute 1 into 2 . We get Area A 3(1) 3

4

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SAT PRACTICE TEST 1 – SECTION 2 ANSWERS • 621

13.

Substitute 1 into 3 . We get 1 3(Area C) 1 Area C 3 Using 1 , 4 and 5 , we have

5

y2 y1 Choice B is correct. Slope is defined as x2 x1 where (x1, y1) is a point on the line and (x2, y2) is another point on the line. We are given that one point is (0, p) and the other point is (3p, 0) so, 1 y2 y1 p0 p 3 x2 x1 0 3p 3p

1 Sum of areas A, B and C 3 1 3 1 Sum of areas A, B and C 4 3



14.



40 km Given: Bus A averages gallon

1

50 km Bus B averages gallon

2

Trip distance 800 km 3 $3 Fuel cost 4 gallon (Use strategy 10: Know how to use units.) Given: PQR 9 PQ 4

1 2

(Use Strategy 3: The whole equals the sum of its parts.) From the diagram, we see that PQR PQ QR

3

Substitute 1 and 2 into 3 . We get 9 4 QR 5 QR QR is the radius of a circle with center R and Q on its circumference. (See dot circle in diagram.) (Math Refresher 524) 11.

Choice B is correct. y f(x) is positive or 0 for all x, so only Choices B and C are appropriate. Since y f(x) represents straight lines, then Choice B is appropriate where Choice C is eliminated. (Math Refresher 616 and 615)

12.


Divide 3 by 1 . We get 800 km 800 gallons 20 gallons used 40 km

40

by Bus A

5

gallon Divide 3 by 2 . We get 800 km 800 gallons 16 gallons used 50 km

50

by Bus B

6

gallon Multiply 5 by 4 . We get $3 20 gallons $60 cost for fuel for Bus A gallon

7

Multiply 6 by 4 . We get $3 $48 cost for fuel 16 gallons gallon for Bus B

8

(Use Strategy 13: Find unknowns by subtracting.) Subtract 8 from 7 . We get $60 $48 $12 difference in the fuel costs between Bus A and Bus B for an 800 km trip. (Math Refresher 202)

Given: C is the midpoint of AB Thus, AC CB 1 Substitute the lengths from the diagram into 1 . We have 2a b 3a b b ab 2b a (Math Refresher 406)

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Page 622


15.


17.

Choice C is correct. The probability is the number of favorable ways divided by the number of total ways. The total ways is the number of points in the large circle of radius 2 feet. We can look at that as the area of the large circle which is pr 2 2 2p 4p. The favorable ways are the number of points in the inner circle which we can look at as the area of that circle which is p r 2 1 1p 1p. Thus the probability is 1p /4p 1/4. (Math Refresher 614)

(Use Strategy 17: Use the given information effectively.) Given: m||n 1 From 1 we know that the two angles are supplementary. Thus, (5y 60)° y° 180° 6y 60 180° 6y 240° y 40° (Math Refresher 504) 16.

Choice C is correct. (Use Strategy 2: Translate from words to algebra.) We have: 4 (2a b) 18 1 100 (Use Strategy 13: Find unknowns by multi100 plication.) Multiply 1 by . We get 4 100 4 100 (2a b) (18) 4 100 4

(Use Strategy 19: Factor and reduce.)

4 25 2a b (18) 4

2a b 450 b 450 2a

Choice A is correct. (Use Strategy 18: Remember special right triangles.) The triangle at left (given) is similar to the triangle at right, which is one of the standard triangles. Corresponding sides of similar triangles are proportional. Thus,

2w y

2w x and 2 1 2 3 or

y w and x w 3 Area of rectangle 1/2(base)(height) 1/2(y)(x) 1/2(w)(w 3) 3 Area of triangle w2 2

2

(Use Strategy 17: Use the given information effectively.) b will be greatest when a is smallest. Given: a is a positive integer

18.

3 4

Applying 4 to 3 , we get a1 Substituting 5 into 2 , we have b 450 2(1) 450 2 b 448 (Math Refresher 406)

Area of rectangle (3w)(w) 3w2

1 2

Using 1 and 2 , we have Ar ea of rectangle 3w

2 A rea of triangle 3 w2 2 2 3 3 3 3 2 6 3 6 2 3 3 3 or 2 3 : 1 (Answer) (Math Refresher 510, 509, 306, and 304)

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19.

Choice B is correct. (Use Strategy 2: Translate from words to algebra.) Let f Number of freshmen s Number of seniors We are given f 3s 1 1/4 of the freshmen f 4 1 1/3 of the seniors s 3 Total number of freshmen and seniors f s

1 2

Substituting 4 into 2 and into 3 , we get

3

Using 4 and 5 , we have:

4

x 10, z 30

The sum of x y z 10 20 30 60

1 2 3 4

5

6

(Use Strategy 17: Use the given information effectively.)

This is the number of students who have either a car, a bicycle, or both.

The desired fraction uses 2 , 3 and 4 as follows: 1 1 f s 4 3 5 fs

Using 1 and 6 , we get 100 60 40 as the number who have neither a car nor a bicycle nor both.

Substituting 1 in 5 , we get 1 1 (3s) s 4 3 3s s

3 1 s s 4 3 4s

6

Multiplying 6 , numerator and denominator, by 12 we get: 3 1 s s 4 3 12 4s 12

9s 4s 48s 13s 48s 13 48

(Answer)

(Math Refresher 200, 402, and 108) 20.

Total students 100 We are given: x y 30 z y 50 y 20

Choice C is correct. (Use Strategy 2: Translate from words to algebra.) Set up a Venn diagram:

x number of students with only a car z number of students with only a bicycle y number of students having a car and a bicycle

(Math Refresher 200 and 406)

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1.

Choice C is correct. (Use Strategy 17: Use the given information effectively.) Given: 55,555 y 50,505 5,050 y We need: 50,505 10y

3.

We are told that 1 decimeter 100 millimeters (Use Strategy 17: Use the given information effectively.)

1 2

Dividing each height from the table, we get:

Substitute 1 into 2 . We get 50,505 10(5,050) 50,505 50,500 5

1700 (A) 17 100 2450 (B) 24.5 100 2735 (C) 27.35 100 1928 (D) 19.28 100 2130 (E) 21.3 100



Choice D is correct. Using the distributive property, we get 3x(4x 2y) 12x2 6xy (Math Refresher 409)

Note that choices B, C, and E are greater than 20. (Math Refresher 121 and Division)

624

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4.

Choice E is correct Given:

7.

a37

12 must be substituted for P in each of the five expressions and the results evaluated.

1

(Use Strategy 13: Find unknowns by addition, subtraction, and multiplication.)

P 12 P 3 12 3 (P 3 2 (12 3) 2 [(P 3 2] 12 [(12 3) 2] 12 Item 5: [(P 3) 2] 12 1 [(12 3) 2] 12 1

Item 1: Item 2: Item 3: Item 4:

Fast Method: From 1 , we can subtract 7 from both sides, and then add 3 to both sides to get a73

2

Multiplying 2 by 2, 2a 14 6


29


Slow Method: Solve 1 to get a 10

3

8.

Choice E is correct. 3x Given: 9 4

Now substitute 3 : (Answer)

1

(Use Strategy 13: Find unknowns by multiplication.)

(Math Refresher 406 and 431) 5.

30

Item 2 is greatest in value.

(Answer)

2a 14 2(10) 14 6

12 36 18

Multiplying 1 by 4, we get

Choice D is correct. (Use Strategy 17: Use the given information effectively.)

3x 4 (9)4 4 3x 36

Change all fractions to decimal form:

Multiply 2 by 2. We have 2(3x) (36)2 6x 72

7 .7 10 7 .07 100 7 .077 1000


Adding these we get .847 (Answer) (Math Refresher 104) 6.

Choice A is correct. Know the properties of parallel lines. If 2 parallel lines are crossed by a transversal, the pairs of corresponding angles are equal. Thus, xa From the diagram, a y 180

1 2

9.

Choice C is correct. From the diagram we find that AB 2 BC 2 CD 2 DE 2

1 2 3 4

(Use Strategy 3: The whole equals the sum of its parts.) We know AB BC AC

Substituting 1 into 2 , we get x y 180

(Answer)


Substituting 1 and 2 into 5 , we get 2 2 AC

5

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4 AC

(Use Strategy 13: Find unknowns by subtracting.)

6 7

We know CD DE CE Substituting 3 and 4 into 7 , we get 2 2 CE 4 CE

Subtracting 1 from 2 , we get B A 98765 12345 B A 86420 (Logical Reasoning)

8 12.

Choice D is correct. Given: Meteor 1 travels at 300 meters/second Meteor 2 travels at 700 meters/second Draw a diagram:

Filling 6 and 8 into the diagram and using the fact that all the segments drawn were perpendicular, we have ECA is an isosceles right triangle. (Use Strategy 18: Remember the isosceles right triangle.) In the isosceles right triangle, the hypotenuse leg(2)

9

Substituting 6 or 8 into 9 , we get EA 4 2.

6



Two-digit numbers which have a units-digit 0 that can be tripled in value when the tens-digit is tripled are the following:

(Use Strategy 9: Know Rate, Time, and Distance relationship.) Rate Time Distance 300 m/sec t x 700 m/sec t 2500 x

3 4

(Use Strategy 13: Find unknowns by addition.)

5

(Use Strategy 10: Know how to use units.) 1 km 1000 m (1000 m/sec)t 2500(1000)m Divide 7 by 1000 m:

(Logical Reasoning) Choice C is correct. (Use Strategy 11: Use new definitions carefully.) By definition, A 12345 B 98765

(300 m /sec )t (700 m /sec )t 2500 km (1000 m /sec )t 2500 km

Substitute 6 in 5 :

Tripled tens digit number 30 60 90

The above numbers are the only numbers that result in a two-digit number as defined in the problem. Thus, 3 is the correct answer.

11.

Let t be the time it takes meteors to meet. Call x the distance Meteor 1 travels. Then 2500 x is the distance Meteor 2 travels.

Add 3 and 4

(Use Strategy 11: Use new definitions carefully.)

Original number 10 20 30

1 2

1 2

t/sec 2500 t 2500 sec (Math Refresher 121, 201, and 202)

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13.


We have Sum of first 4 positive integers 3a 3 a 3 4a 6

(Use Strategy 17: Use the given information effectively.) The center point inside a cube is the midpoint of an inner diagonal of the cube. Thus, the distance from any vertex to this center point is 1 length of the inner diagonal. 2 We know length of inner diagonal of a cube

Since 3 can be written as 2(2a 3), it is divisible by 2. Thus, if the number of integers is a multiple of 4, the sum of the consecutive positive integers will be divisible by 2.

(edge )2 (e dge)2 (ed ge)2 inner diagonal 3(edg e)2

1

inner diagonal edge 3

2

Given:

Volume 8 cubic meters

We know volume of a cube (edge)3

3 4

Substituting 3 into 4 , we get 8 cubic meters (edge)3 3

5

Substituting 5 into 2 , we get inner diagonal (2)3 inner diagonal 23 meters

6

Using 1 and 6 we find 1 distance we need (inner diagonal) 2 1 (2

3 meters)

2 meters 3 Distances we need 3 m

(Use Strategy 2: Translate from words to algebra.) Let a a positive integer Then a 1, a 2, a 3, a 4, etc., are the next positive integers. (Use Strategy 13: Find unknowns by addition.)

1

Given: Square has perimeter 2p Let S side of square. We know Perimeter of a square 4S

2

Perimeter of square 4S 2p 4S 2p S 4 p S 2 We are given that: area of circle area of square We know that: area of circle pr 2 area of square S2

3 4 5 6

pr 2 S2

7

p pr 2 2

2

p2 pr 2 4 p2 r 2 4p p r 2 4

1

1 is not divisible by 2. Now add the third positive integer, a 2, to 1 . We get Sum of first 3 positive integers 2a 1 a 2 3a 3

Choice B is correct. (Use Strategy 2: Translate from words to algebra.)



Add the first 2 positive integers. We get Sum of first 2 positive integers a a 1 2a 1

15.

Substituting 5 and 6 into 4 , we get




3

c 8 cubirs mete (edge )3 2 meters edge

3

2

2 is not divisible by 2. Now add the fourth positive integer, a 3, to 2 .

p p r 4 2

8

We know the circumference of a circle 2p r Substitute 8 into 9 . We have

p Circumference p 2

2

Circumference pp (Math Refresher 303 and 310)

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16.

We know: Rate Time Distance Substitute 1 and 4 into 5 . We get

Choice E is correct. Given: a 1 b 4

1

x km 1 y hours Distance hour 3 xy 2 Distance plane had flown y hours ago. 3 3

(Use Strategy 13: Find unknowns by multiplying.) Cross-multiply 1 . We have 4a b a2 Substituting 4a b in the given , we get b 2 2 a a a 4a b 4

2

(Use Strategy 7: Use numerics to help find the answer.) If a 1 is substituted into 3 we have a2 a 1 b 4 4 Thus, Choice I is satisfied. If a 2 is substituted into 3 , we get a2 a 2 1 b 4 4 2

Thus Choice III is satisfied.

We know that Average Sum of values Total number of values Given: Average of k scores is 20 Substitute 2 into 1 . We get Sum of k values 20 k 20k Sum of k values

Choice B is correct. (Use Strategy 2: Translate from words to algebra.)

1 2

2 Need: Distance plane had flown y hours 3 ago 3 Subtracting 3 from 2 , we get 2 2 Time plane had flown y hours ago y y 3 3 2 Time plane had flown y hours ago 4 3 1 y hours 3 (Use Strategy 9: Know the rate, time, and distance relationship.)

1 2

3 4

Substitute 4 into 1 . We have

There are k 10 scores remaining.


Time of flight y hours

(Use Strategy 5: Average Sum of values Total number of values

Sum of 10 scores 15 10 150 Sum of 10 scores

a2 a 4 1 b 4 4

Given: Rate of plane x km hour


Given: Average of 10 of these scores is 15.

Thus, Choice II is satisfied. If a 4 is substituted into 3 , we have

17.


3

5

5 6

(Use Strategy 3: The whole equals the sum of its parts.) We know: Sum of 10 scores Sum of remaining scores Sum of k scores 7 Substituting 3 and 5 into 7 , we get 150 Sum of remaining scores 20k Sum of remaining scores 20k 150 Substituting 6 and 8 into 1 , we get 20k 150 Average of remaining scores k 10 (Math Refresher 601)

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19.

Choice E is correct. Given: Area of square R Perimeter of equilateral triangle E Perimeter of square r Side of equilateral triangle e 2

1 2 3 4

When the Centigrade temperature increases by 35°, the Fahrenheit temperature increases by x°, so we get: 5 C 35 [(F x) 32] 9

(Use Strategy 17: Use the given information effectively.) We know Perimeter of square 4(side) We know Area of square (side)2 Substituting 1 into 6 , we get

5 6

5 5 5 C 35 F x (32) 9 9 9

(Now use Strategy 13: Find unknowns by subtraction.) Subtract 1 from 2 :

R2 (side)2 R side

7

5 5 5 C 35 F x (32) 9 9 9

Substituting 7 and 3 into 5 , we have r 4(R) r 4R

8

We know Perimeter of equilateral triangle 3(side)

5 5 C F (32) 9 9 5 35 x 9

10

We need e r

11

(Use Strategy 13: Find unknowns by addition.) Add 8 and 10 to get 11 . We have

E 3 4R 3 3

4

(Use Strategy 19: Don’t multiply when reducing can be done first.) Divide 4 by 5: 35 9 x 5

5


E 12R 3 3 E 12R e r 3 (Math Refresher 303 and 308) Choice D is correct.

1

Call the number of degrees that the Fahrenheit temperature (F°) increases, x. (Now use Strategy 17: Use the given information effectively.) The Centrigrade temperature (C°) is given as 5 C (F 32) 9

3

35 Now reduce to get 7 and we get for 5 5 7 9x 63 x

E e r 4R 3

5 Given: C (F 32) 9

1

Multiply 3 by 9: 35 9 5x

E 3(e) E 3e E e 3

2

9


20.

2

1

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Page 630

Explanatory Answers for SAT Practice Test 1 (continued) Section 4: Critical Reading As you read these Explanatory Answers, you are advised to refer to “Using Critical Thinking Skills in Verbal Questions” (beginning on page 118) whenever a specific Strategy is referred to in the answer. Of particular importance are the following Master Verbal Strategies: Sentence Completion Master Strategy 1—page 118. Sentence Completion Master Strategy 2—page 119. Reading Comprehension Master Strategy 2—page 136. Note: All Reading questions use Reading Comprehension Strategies 1, 2, and 3 (pp. 133–138) as well as other strategies indicated.

1.

Choice D is correct. See Sentence Completion Strategy 4. The first word, “Because,” is a result indicator. We can then expect some action to take place after the information about what the evening cable TV programs deal with. The expected action is that parents will consider such programs “inappropriate.” Accordingly, only Choice D is correct.

2.

Choice A is correct. See Sentence Completion Strategy 2. Examine the first word of each choice. Choice (C) glamorized . . and Choice (D) viewed . . do not make good sense because a word does not effectively glamorize or effectively view unfairness. Now consider the other choices. Choice (A) portrayed . . strengthening is the only choice which has a word pair that makes sentence sense.

3.

Choice E is correct. See Sentence Completion Strategy 1. The word “prolific” (meaning “producing abundant works or results”) completes the sentence so that it makes good sense. The other choices do not do that.

4.

Choice D is correct. Although this is a two-blank question, we should use Sentence Completion Strategy 1 (primarily used for one-blank ques-

tions). Note that we have a set of three opposites: from the “serious” to the “lighthearted,” from the “objective” to the “argumentative,” and from the “innocuous” (meaning harmless, innocent) to the “hostile.” The other choices do not have this opposite pattern.

630

5.

Choice B is correct. See Sentence Completion Strategy 2. Examine the first word of each choice. Choice (A) shattering . . and Choice (C) impertinent . . do not make sense because rates at a repair place are not aptly called shattering or impertinent. Now consider the other choices. Choices D and E do not make sense in the sentence. Choice (B) exorbitant . . instituted does make sense.

6.

Choice E is correct. See Sentence Completion Strategy 2. Examine the first word of each choice. Choice (B) denied . . and Choice (D) slighted . . do not make sense because students who found truth in Socrates’ teachings would not deny or slight him. Now consider the other choices. Choice (A) accepted . . a benefit and Choice (C) appraised . . an exception do not make sense in the sentence. Choice (E) revered . . a threat does make sense in the sentence.

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7.

Choice B is correct. See Sentence Completion Strategy 1. Try each of the choices. The only one that fits is choice B: The quotation was erroneously ascribed, or credited to, a British poet.

8.

Choice D is correct. See Sentence Completion Strategy 2. Examine the first words of each choice. We eliminate Choice (C) squandered and Choice (E) regaled because hardworking parents do not squander (spend money recklessly) or regale (entertain) to give their son an education. Now consider the other choices. The word pairs of Choice A and Choice B do not make sense in the sentence. Choice (D) struggled . . generously does make good sense.

16.

Choice A is correct. See the next-to-last paragraph: “With the over-exploitation of the particular car comes an increased demand . . . to endow the petroleum magnates . . . with fabulous capacities for personal luxury . . .”

17.

Choice C is correct See the next-to-last paragraph: “With the over-exploitation of the particular car comes an increased demand . . . to roll ever wider carpets of concrete over the bulldozed landscape . . .”

18.

Choice B is correct. See the last paragraph: “. . . If indeed we go farther and faster along this route, there is plenty of evidence to show that the shop will close up without our help.”

19.

Choice B is correct. From the context of the paragraph we are talking about distances. Don’t get lured into Choice C because you read about “human needs” in the paragraph or Choice D just because you see “traffic” mentioned. See also Reading Comprehension Strategy 5.

20.

Choice D is correct. From lines 28–32 and other sections of the passage, we can see that the author believes that “technocratic” thinking neither addresses nor is concerned with real human needs.

21.

Choice A is correct. See paragraph 6: “If we took human needs seriously . . . we should make the fullest use of pedestrian movement . . .”

22.

Choice C is correct. See paragraph 5: “. . . Variety of choices, facilities and destinations, not speed alone, is the mark of an organic transportation system.”

23.

Choice B is correct. Judging from the timeperspective of the author, and the more general nature of the article, Choice B would be the best answer.

24.

Choice C is correct. See paragraph 5: “. . . And [variety] is an important factor of safety when any part of the system breaks down.”

9. (E) See lines 5–6 and lines 10–12. 10. (D) in the context, you can see that “extenuate”

means to excuse. See Reading Comprehension Strategy 5. 11. (E) See lines 4–8: “Richness in poetic imagery . . .”

and lines 10–13: “Even his elaborate and multistranded plots . . .” 12. (E) See lines 10–13 which describe the forceful-

ness and power up to the closing. 13.

14.

15.

Choice B is correct. See the first paragraph: “Many people who are willing to concede that the railroad must be brought back to life are chiefly thinking of bringing this about . . . by treating speed as the only important factor . . .” Choice D is correct. See the fourth paragraph: “The prime purpose of passenger transportation is not to increase the amount of physical movement but to increase the possibilities for human association cooperation, personal intercourse and choice.” Choice E is correct. See paragraph 6: “. . . The current introduction of shopping malls . . . is a . . . far better technical solution than the many costly proposals for introducing moving sidewalks or other rigidly automated modes of locomotion.”

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Explanatory Answers for Practice Test 1 (continued) Section 5: Writing For further practice and information, please refer to Grammar and Usage Refresher starting on p. 461. 1. (A) Choice A is correct. Choice B is awkward. The

7. (B) The key to getting the correct answer in this

parenthetical effect of Choice C gives the sentence an ungrammatical structure. The ellipsis of “to the” before the beginning of Choice D, is improper. The possessive use (“oak’s”) in Choice E results in a bad-sounding sentence.

Choice B is incorrect. Choices C, D, and E change the meaning of the original sentence.

question is knowing this grammatical rule: When explanatory words intervene between the subject and the verb, the number or person of the real subject is not changed. Note that the subject “father” of the original sentence is singular. Accordingly, Choices A, C, D, and E (each of which has a singular subject, “father”) are incorrect with a plural verb. Moreover, Choice D changes the present time of the original sentence to past time. Choice B is correct.

3. (D) Choices A, B, and E are too wordy. Choice C

8. (E) The demonstrative adjective (“this,” “that,”

changes the meaning of the original sentence. Choice D is correct.

“these,” “those,”) must agree in number with the noun (“kind”) it modifies. Accordingly, Choices A, B, and D are incorrect. Choice C is incorrect because the personal pronoun “them” may not be used as an adjective. Choice E is correct.

2. (A) Choice A is correct. The present tense in

4.

(D) Choice A does not come to the point immediately with the use of the expression “concerning the one.” Choice B is too wordy. Choice C is not clear. Choice D is correct. Choice E requires an introductory prepositional compound such as “as to.”

9. (D) Choices A, B, C, and E are incorrect because

they suffer from incomplete verb comparison. This is a form of improper ellipsis. The corrections would be as follows: Choice A—“has not recovered”; Choice B—“never will recover”; Choice C— (two corrections necessary) “has not recovered” and “never will recover” (the subjunctive “would” should not be used here); Choice E—“has not recovered.” Note that in Choice E, the past perfect tense should not be used. Choice D is correct.

5. (C) Choices A, B, D, and E are incorrect because of

a dangling participle error. In these four choices, the participle “Having” must refer to the subject of the sentence. This subject must follow directly after the participial construction (“Having . . . in his class,”). Accordingly, Choice C is the only correct choice. 6. (C) Choice A is incorrect because “its” as a posses-

sive pronoun does not take an apostrophe. Choice B is incorrect because the possessive of “government” (“government’s”) must be used to modify the gerund “failing.” Choice C is correct. Choice D is incorrect for the same reason that Choice B is incorrect. Choice E is incorrect for two reasons: (1) it changes the meaning of the original sentence; (2) even if we change the meaning from singularity to plurality, “governments” must correctly be the possessive form “governments’” to modify the gerund “failing.”

10. (D) It is important to know that “neither-nor” go

together as correlative conjunctions. The pairing of “neither” with “or” is incorrect. Therefore, Choices A, C and E are incorrect. Choice B is awkward. Choice D is correct. 11. (A) Choice A is correct. Note that “Glory” is the

singular subject which takes the singular verb “is.” “Reward” is the predicate nominative after the copulative verb “is.” The other four choices are incorrect because they are indirect and awkward. 632

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SAT PRACTICE TEST 1 – SECTION 5 ANSWERS • 633 12. (B) “. . . disappeared as if . . .”

The correct expression is “as if ”—not “like as if.” Incidentally, Choice C (were) is correct because it is the correct form of the contrary-to-fact conditional.

23. (A) “Had Lincoln been alive . . .”

In a past contrary to fact situation, the “if clause” verb should take the form had been—not had have been. 24. (E) All underlined parts are correct.

13. (D) “. . . because the car needed gasoline. The pro-

noun it has an indefinite antecedent. We cannot tell whether it refers to the car or the ser vice station. Accordingly, we must be specific by using car instead of it. 14. (A) “The man whose temper is under control . . .”

The contraction (who’s meaning who is) is obviously incorrect here. We need the possessive pronounadjective whose to modify the noun (temper). 15. (E) All underlined parts are correct. 16. (C) “. . . before his mother came home . . .”

The past perfect tense (had come) is used for a past action that occurs before another past action. The mother’s coming home did not occur before Bob wanted to finish his homework. Therefore, the past tense (came) should be used—not the past perfect tense (had come).

25. (E) All underlined parts are correct. 26. (A) “It’s my opinion . . .”

We need the contraction here (It’s meaning It is). 27. (A) “If I had known more . . .”

The “if clause” of the past contrary-to-fact conditional statement requires the had known form—not the would have known form. 28. (D) “If you compare Bill and Joe . . . Bill is, without

any question, the brighter.” In comparing two individuals, we use the comparative form (brighter)—not the superlative form (brightest). 29. (B) “In spite of how poorly Ellen had done . . .”

The adverb ( poorly)—not the adjective ( poor)— must be used to modify the verb (had done).

17. (B) “Inflation together with the high interest rates

30. (B) Choice A is incorrect: The removal of the con-

and soaring oil prices is hurting . . .” The subject of the sentence is Inflation. This is a singular subject so the verb must be singular—is hurting (not are hurting). The words rates and prices are not parts of the subject.

junction and replacement with a comma would leave two independent clauses incorrectly joined with only a comma. Choice B is correct: Replacing “moreover” and surrounding punctuation with “when” would correctly make the second clause subordinate to the first and also establish a time sequence for the two pieces of information. Choice C is incorrect because omitting “the Persian leader” would result in an information gap about who Cambyses was. Choice D is incorrect in that “bull-headedness” indicates irrational stubbornness and is, therefore, not an accurate description of the motives of people defending their own city in battle; “fierce resistance” is more appropriate. Choice E is incorrect because “moreover” (meaning “beyond what has been stated, further, or besides”) does not furnish an adequate transition between the idea of the first sentence and the idea of the second sentence which need to be related to each other in a time sequence. The comma— instead of the semicolon—would be incorrect punctuation preceding the conjunctive adverb.

18. (D) “. . . will repair the car well.”

The adverb (well )—not the adjective (good )—is used to modify the verb (will repair). 19. (C) “. . . if he had read more . . .”

The “if” clause of a contrary-to-fact past tense requires the verb had read—not would have read. 20. (D) “. . . to have his stories compared with those of

Dickens.” We have an improper ellipsis in the original sentence. The additional words (those of ) are necessary to complete the meaning of the sentence. 21. (B) “. . . with a new type of motor . . .”

Do not use the article a or an after kind of, type of, sort of, etc.

31. (D) Choice A is incorrect because the introduction 22. (A) “Sharon planned to pay about . . .” About means

approximately; around means on all sides.

of “It was made worse” would create a run-on sentence. Choice B is incorrect in that omitting the phrase would remove a needed transition to carry

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the action from sentence four to sentence five by indicating that a second tactic was used. The phrase also furnishes some dramatic reinforcement of the idea that the Egyptians were “appalled.” Choice C is incorrect because “plus” can be used as an adjective or a preposition but not, as in this sentence, as a conjunction. Neither the meaning “in addition to” or “added” fits the structure of the sentence. Choice D is correct because the phrase is useful as a transition and for emphasis. (See explanation for Choice B.) Choice E is incorrect in that placing the phrase at the end of the sentence deprives the phrase of its use as a transition between sentences five and six.

graph, even with an appropriate change in the verb to “had ordered,” the sentence would furnish anticlimactic information, well after the time the data was needed. Choice D is incorrect because beginning a new sentence after “countryside” would leave the remaining words as a sentence fragment. Choice E is incorrect not only because it would leave sentence six in a position in which chronology is not clearly indicated, but also because inserting “which was because” creates unnecessary wordiness and a pronoun with an ambiguous reference while leaving “ordered” in the wrong tense. 34. (B) Choice A is incorrect: “capitulated” is an accu-

32. (D) Choice A is incorrect: “unharmed without

hurting them” is redundant; adding “in the least little way” would only compound the repetition. Choice B is incorrect since the redundancy would remain. Choice C is incorrect: The sentence would lose clarity without the information that the soldiers were to keep the cats safely. Choice D is correct because omitting “without hurting them” would cure the redundancy. Choice E is incorrect because the base words “hurt” and “harm” would be merely reversed without eliminating the repetition weakness. 33. (A) Choice A is correct: The proper place for sen-

tence six is after sentence three. In that position, sentence six would show the chronological order of events correctly and the tense of “ordered” would be accurate. Choice B is incorrect since the omission of the sentence would leave a puzzling information gap about where the cats came from. Choice C is incorrect: Placed at the end of the para-

rate synonym for “surrendered”, while “crumbled” would suggest the physical decay of the city walls or buildings. Choice B is correct: Since previous battle has been suggested in sentence three (“the Persian army . . . blocked by the fierce resistance”), sentence eight would be more accurate if it ended with “further battle.” Choice C is incorrect because, as noted, the Egyptians had previously fought the Persians. Choice D is incorrect: Even though “having resisted” is a complete idea and far preferable to the incomplete idea of “a drop of blood,” the substitution is still inaccurate because the Egyptians had previously resisted. Choice E is incorrect because it conveys a totally inaccurate idea of the reason for the surrender of Pelusium. 35. (C) Since sentence 8 is general (not specific)

describing animal worship, this would lead directly to sentence 1 which is more specific, especially because of the words “In fact” at the beginning of

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Explanatory Answers for Practice Test 1 (continued) Section 6: Math As you read these solutions, you are advised to do two things if you answered the Math question incorrectly: 1. When a specific Strategy is referred to in the solution, study that strategy, which you will find in “Using Critical Thinking Skills in Math Questions” (beginning on page 69). 2. When the solution directs you to the “Math Refresher” (beginning on page 191)—for example, Math Refresher #305—study the 305 Math principle to get a clear idea of the Math operation that was necessary for you to know in order to answer the question correctly.

1.

dinates are (5,2), then m ⭿MXN 90° and Choice E must be correct.

Choice D is correct. Method 1: (Use Strategy 8: When all choices must be tested, start with Choice E.) Since x is odd, then x is odd. Let us start with solution E.


1 3.

Choice E: If x is odd (from 1 above), then x2 is odd. Choice D: If x is odd, 2 x is even, and the solution is found. (Use Strategy 7: Use numerics to help you get the answer.)

(Math Refresher 616, 702)

Method 2: Choose an odd number for x —for example,

4.

x 3 Then x 9 Choice E x2 81 (odd) Choice D 2x 2(3) 6 (even)

Choice D is correct. Since (according to the graph), y 0 when x 0, Choices A, B and E are incorrect. Choice C is incorrect since the graph is not a parabola. The only feasible choice is Choice D. (Math Refresher 410)

The answer is clearly Choice D.

5.

(Math Refresher 430 and 431, and 603) 2.

Choice D is correct. You want to find a value of x such that f(x) x 2, so you look for a value of x in the x-column that makes f(x) in the f(x) column, x 2. You can see that x 3 corresponds to f(x) 5 which is just x 2 (or 3 2).

Choice E is correct. (Use Strategy 8: When all choices must be tested, start with Choice E.) Since we must check all the choices, we should start with Choice E. Clearly, if x is the point whose coor-

Choice E is correct. (Use Strategy 2: Translate from words to algebra.) The sum of the degree measures of the 4 angles of any quadrilateral is always 360. Therefore, w x y z 360°

635

1

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(Use Strategy 5: Average Sum of values Total number of values

5 feet/second 9,000 seconds 45,000 feet

Dividing by the circumference of 120 feet, we have 45,000 feet number of revolutions 120 feet/revolution

If w is the average (arithmetic mean of x, y, and z, then xyz w 3

Use a calculator for the above or use Strategy 19: Factor and reduce.

Multiplying both sides of the above equation by 3, we have

3 15 10 25 4 3 4 10

3w x y z

Substituting equation 2 into equation 1 , we get or or

375 revolutions (Answer) (Math Refresher 200, 201, and 202)

2 8.

w 3w 360° 4w 360° w 90°

From equation 2 , we conclude that x y z 3w 3(90) 270°

Area of triangle Area of square x2 3 x2 x2(3 1)


We are given that an unknown rectangle has width x and area x 2(3 1)

Choice B is correct. (Use Strategy 17: Use the given information effectively.) The circle graph tells you that 19% of this mixture is carbon. Since the total mixture weighs 24 pounds, 19% of that will be the amount of carbon in the mixture (in pounds). We would multiply 24 lbs .19. But since we are looking for the closest number of pounds, make the problem simpler by multiplying 24 .20 4.8.

Choice B is correct. (Use Strategy 2: Translate from words to algebra.) Each complete revolution is one circumference. one circumference 120 feet B completed 600 revolutions. Total distance (600 revolutions)(120 feet/revolution) Total distance 600 120 feet (Use Strategy 9: Know the rate, time, and distance relationship.) Total distance Time for B Rate 600 120 feet 8 feet/second Use a calculator for the above or use Strategy 19: Factor and reduce. 600 8 15 feet 8 feet/second Time for B 9,000 seconds A traveled at 5 feet/second A’s total distance is

1 2

Since length width area, length area width 3 Substituting 1 and 2 into 3 , we have x2(3 1) length of rectangle x


Choice D is correct. The key to this problem is to find the area of the shaded region in terms of known quantities. (Use Strategy 3: The whole equals the sum of its parts.) Area of shaded region and also the area of the rectangle

length of rectangle x(3 1) (Math Refresher 303, 304, and 306) 9.

7/24, 2/7, or any number between 0.25 and .3333. (Use Strategy 17: Use the given information effectively.) Without a calculator: 3 1 Get a common denominator 12. Then write 12 4 4 3 4 1 and to get a quantity in between and . 12 12 12 3 3 6 4 8 Write and 12 24 12 24 6 8 7 Thus x and x can be . 24 24 24 1 2 1 2 2 2 2 2 Or write and . , so is an 4 8 3 6 8 7 6 7 answer. With a calculator: 1 1 Calculate 0.25; Calculate 0.3333. . . . 4 3 “Grid” any number between 0.25 and 0.3333 like 0.26, 0.27 . . . . .332, .333. (Math Refresher 419)

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10.

We know that in triangle RST

12 Given: 3x y 17 x 3y 1

1 2

ⱔ RST ⱔ SRT u 180°

9

Substitute 2 and 8 into 9 . We get (Use Strategy 13: Find unknowns by adding.)

80° 40° u 180° 120° u 180° u 60°

Adding 1 and 2 , we get 4x 4y 16

3

(Use Strategy 13: Find unknowns by division.) Dividing 3 by 4. We have xy4


4

(Use Strategy 13: Find unknowns by multiplying.) Multiply 4 by 3. We get

22 people

1 5 trips 2 4 p eople trip (Use Strategy 16: The obvious may be tricky!) 1 1 There is no such thing as a trip. The arises 2 2 because the last trip, the 6th trip only, takes 2 people.

3x 3y 12 (Math Refresher 407) 11.

6 (Use Strategy 17: Use the given information effectively.) If the tram carries its maximum of 4 people then

60

1

1 The represents 2 people 2 2 4 p eople trip There are 5 trips at 4 people each 20 people 1 trip at 2 people 2 people TOTAL 6 trips totaling 22 people Given: ⱔ M 120° ⱔ RST 80°

13.

(Use Strategy 3: The whole equals the sum of its parts.) From the diagram we see that ⱔ RST w w

3

5

6

From the diagram we see that ⱔ SRT v v

7

Substitute 6 into 7 . We get ⱔ SRT 20° 20° ⱔ SRT 40°

1 2

a 䉺 b (a b)2 (a b 2) a2 2ab b2 (a2 2ab b 2) 4ab 3 When we use 3 , we get

Substituting 4 into 5 , we get v 40° 120° 180° v 160° 180° v 20°

(a b)2 a2 2ab b2 (a b)2 a2 2ab b2

Using 1 and 2 , we have 4

We know that in triangle RMS v w 120° 180°

24 Method 1: (Use Strategy 4: Remember classic expressions.)

(Use Strategy 11: Use new definitions carefully. These problems are generally easy.)

Substitute 2 into 3 . We get 80° w w 80° 2w 40° w

(Logical Reasoning)

1 2

8

)(2 ) 18 䉺 2 4(18 4(36 ) 4(6) 24 Method 2: a 䉺 b (a b)2 (a b)2 18 䉺 2 (18 2 )2 (18 2 )2 18 2 36 2 (18 2 36 2) 18 12 2 18 12 2 24

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n(n 1) It is 2

The calculations in Method 2 are much more complex!

Substituting 4 into 1 , we get


1

4(4 1) 4(3) 2 2 12 6 2

25 If you have patience, it is not too hard to list all ordered pairs of integers (x, y) such that x2 y2 9

(Logical Reasoning) (Use Strategy 17: Use the given information effectively.)

16.

Another way to do this problem is to note that x2 y2 9 is the equation of a circle of radius 3 whose center is at (0, 0).

35 (Use Strategy 2: Translate from words to algebra.) The boy originally had enough money to buy 21 bars at 50¢ per bar. Thus, he had 21 50 1,050 cents $10.50. Therefore, Number of 30¢ bars he bought Total amount he had Price of each bar $10.50 $ .30 35 bars (Answer) (Math Refresher 200 and 406)

17.

333 (Use Strategy 16: The obvious may be tricky!) From the problem, we see that d 96,999; not 97,777

Thus, x2 y2 9 is the region inside the circle. We want to find the number of ordered pairs of integers (x, y) inside the circle. As we can count from the picture above, there are 25 such ordered pairs. (Math Refresher 410 and 431)

Thus, d 96,666 333 (Logical Reasoning) 18.

1 or .125 8 (Use Strategy 2: Remember the definition of percent.) 25 percent of 2 is 25 2 100 Thus, 25 percent of 25 percent of 2 is 1 1 25 25 2 2 4 4 100 100 2 16 1 8

15.

6 (Use Strategy 17: Use the given information effectively.) Method 1: You can just take out one line and you will have 6 points (see above). Method 2: There is a formula for finding the maximum number of points of intersection of n straight line segments.


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Explanatory Answers for SAT Practice Test 1 (continued) Section 7: Critical Reading As you read these Explanatory Answers, you are advised to refer to “Using Critical Thinking Skills in Verbal Questions” (beginning on page 118) whenever a specific Strategy is referred to in the answer. Of particular importance are the following Master Verbal Strategies: Sentence Completion Master Strategy 1—page 118. Sentence Completion Master Strategy 2—page 119. Reading Comprehension Master Strategy 2—page 136. Note: All Reading questions use Reading Comprehension Strategies 1, 2, and 3 (pp. 133–138) as well as other strategies indicated.

1.

Choice E is correct. See Sentence Completion Strategy 1. Try each choice. He tried his hardest to maintain his calm, or poise.

2.

Choice A is correct. See Sentence Completion Strategy 2. Examine the first word of each choice. Choice (B) a specter . . and Choice (C) an exodus . . ‘do not make sense because a nice apartment building is not a specter (ghost) or an exodus (a departure). Now consider the other choices. Choice (A) a boon . . haunted is the only choice that makes sense in the sentence. The word “haunted” here means “visited frequently.”

opposition indicator. After the subordinate clause “although . . markedly,” we can expect an opposing idea in the main clause that follows and completes the sentence. Choice (B) unaffected gives us the word that brings out the opposition thought that we expect in the sentence. Choices A, C, D, and E do not give us a sentence that makes sense. 5.

Choice D is correct. See Sentence Completion Strategy 1. The word “elusive” means “cleverly or skillfully; able to avoid being caught.” Therefore, Choice (D) elusive is the only correct choice.

6. Choice B is correct. In line 24, the statement, “the 3.

4.

universe does not play dice with nature,” illustrates that Einstein believes that there is certainty and not mere probability in all aspects of physics.

Choice A is correct. See Sentence Completion Strategy 2. Examine the first word of each choice. Choice (B) cancellation . . and Choice (D) abundance . . do not make sense because we do not refer to an inflation cancellation or an inflation abundance. Now consider the other choices. Choice (A) spiral . . indubitably (meaning unquestionably, certainly) is the only choice which has a word pair that makes sentence sense.

7. Choice A is correct. See lines 4–6 and lines 17–19

about measurement devices. Choice B is incorrect because in lines 20–21, we may know the exact position of an electron but not its exact speed. Choice C is incorrect: See lines 28–30. Choice D is incorrect because in lines 4–6, it just describes that the apparatus does not interfere with measurement, not that we don’t deal with measurement.

Choice B is correct. See Sentence Completion Strategy 4. The first word, “although,” is an 639

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640 • SAT PRACTICE TEST 1 – SECTION 7 ANSWERS 8. Choice A is correct. Since classical and modern

13.

Choice E is correct. In the context in the sentence “. . . under the glowing sun . . . ,” it would appear that the word “frenetic” should mean “frantic.” Choice A is incorrect because the author would not be likely to repeat the word “colorful” in the next sentence.

14.

Choice C is correct. Gauguin’s attitude of tolerant acceptance of van Gogh is indicated in the following lines of the passage. Lines 37–41: “At first . . . rather than actuality.” Lines 44–49: “Gauguin wrote to Theo . . . especially with me.” Lines 50–52: “But then . . . they later had friendly correspondence.”

physics seem to be somewhat contradictory, there could exist a “unified” physics that would incorporate both without retaining the paradox’s inherent in classical and modern physics. The other choices do not resolve the issue. 9.

10.

11.

12.

Choice D is correct. For (i), it is seen that cause and effect exist in classical physics but not in modern physics; for (ii), probability exists in modern physics whereas certainty exists in classical physics; for (iii), the structure of a bridge is apparent in both modern and classical physics since subatomic make up the bridge and the macroscopic structure of the supports, etc. also exists. Thus only (i) and (ii) are true and Choice D is correct. Choice A is correct. The passage deals mainly with van Gogh’s 15-month stay in Arles. It was in this small French town that his art, in fact, did reach its zenith. See lines 4–9: “Yet Arles . . . in the modern era.” Although Choices B, C, D, and E have some association with the passage, none of these choices represents the best title for the passage as a whole. Therefore, these choices are incorrect. Choice D is not stated nor is it implied in the passage. Therefore, it is the correct choice. First seelines 42–45: “Before the year was up . . . had to return to Paris.” Note that Gaugin had stayed in Arles less than a year. Now see lines 4–9: “Yet Arles was also the scene . . . in the modern era.” Choice A is true—therefore an incorrect choice. See lines 12–16: “The Arles canvases, alive with color . . . notably the Fauves.” Choice B is true—therefore an incorrect choice. First see lines 17–20: “Van Gogh went to Arles . . . beloved younger brother Theo . . . an art dealer.” Now see lines 39–41: “Gaugin had an influence on van Gogh . . . pushing the younger artist . . . than actuality.” Choice C is true—therefore an incorrect choice. See lines 20–23: “In Paris . . . Neo-Impressionist . . . style.” Choice E is true—therefore incorrect. See lines 1–4: “It was at Arles . . . cut off part of his own ear.”

Choices A, B, D, and E are incorrect because the passage does not give evidence of the attitudes mentioned in these choices. 15.

Choices B and E are incorrect because these were not the basic reasons for van Gogh’s extreme action. The basic reason was van Gogh’s mental and emotional instability (Choice D). Choice C is incorrect because the passage mentions nothing about van Gogh’s failure to form an artists’ colony in Arles. 16.

Choice C is correct. The theme of this essay, SelfReliance, by the American writer Ralph Waldo Emerson (1803–1882), is expressed in various other ways throughout the essay. For example: in referring to the independence of opinion that one loses with one’s loss of early youth; in condemning our surrender of the freedom of solitude to the group actions of society at large; and in encouraging us not to fear the consequences of being inconsistent and misunderstood.

17.

Choice A is correct. The infant can be, and is expected to be, completely irresponsible. “Infancy conforms to nobody: all conform to it, so that one babe commonly makes four or five out of the adults who prattle and play to it.”

Choice E is correct. Let us consider each of the three Roman numeral items. Item 1 is true. See lines 25–27: “But he wanted ‘gayer’ colors . . . Japanese prints he so admired.” Item II is true. First see lines 28–30: “He felt that in Arles . . . establish an artistic tradition.” Now see lines 31–33: “It was van Gogh’s hope . . . join him at Arles.” Item III is true. See lines 27–30: “Then, too, the French capital . . . an artistic tradition.” Accordingly, Choice E is the only correct choice.

Choice D is correct. The passage indicates that there was a buildup of stresses and strains on van Gogh that he was eventually unable to cope with because of his mental and emotional instability. This condition led him to such acts as cutting off a piece of his ear. Finally—though the passage does not include this fact—van Gogh committed suicide in Paris on July 29,1890, by shooting himself in the chest. The following lines in the passage are related to van Gogh’s mental and emotional instability. Lines 1–3: “It was at Arles . . . had his first real bout with madness.” Lines 17–20: “Van Gogh went to Arles . . . supported him psychologically and financially . . . art dealer.” Lines 44–46: “Gauguin wrote to Theo . . . ‘temperamental incompatability.’ ”

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SAT PRACTICE TEST 1 – SECTION 7 ANSWERS • 641 18.

19.

Choice D is correct. “Speak what you think now in hard words; and to-morrow speak what you think in hard words again, though it contradicts everything you said to-day.” The misunderstanding will occur because what you say may be the opposite of conventional opinion, or may be ahead of its time. But the risk is worth it. Choice B is correct. It is a natural prerogative of youth to give “an independent, genuine verdict.” He naturally cares very little about what older people may think because “It seems he knows how to speak to his contemporaries. Bashful or bold, then, he will know how to make us seniors very unnecessary.”

20.

Choice B is correct. The “pit” or gallery in a theater usually contains the least expensive seats. Consequently, it is favored by those less economically endowed, and, according to the author, less committed to conventional manners and highly dignified behavior. In effect, these are the people who go to the theater to see, rather than to be seen.

21.

Choice C is correct. When people desert solitude (or individual action) to join society (group action), they surrender a large part of individual freedom in exchange for a livelihood. They thus become more reliant and dependent on others than on

themselves. The metaphor of the joint-stock company is a good one because such a company is faceless and without identity. No one member stands out above any other member. 22.

Choice E is correct. “Spirit and enthusiasm” are something individualistic and definite. To be spirited and enthusiastic is to be spontaneous, natural, and uninhibited. One must (according to the author) be committed and courageous “As soon as he has once acted or spoken with eclat. . . .” See also Reading Comprehension Strategy 5.

23.

Choice C is correct. To act out of whim is to act impulsively and in an unpremeditated, spontaneous (and generally sincere) manner. The author, however, is not endorsing whimsical action simply because it is uninhibited (“I hope it is somewhat better than whim at last, but we cannot spend the day in explanation”), but because it is a way of speaking freely, and usually with complete honesty.

24.

Choice A is correct. The essence of true self-reliance and genuine nonconformity is, as Shakespeare put it, “To thine own self be true.” If one is dishonest with oneself, one will be dishonest with others; if one is honest with oneself, one will be honest with others.

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Explanatory Answers for Practice Test 1 (continued) Section 8: Math As you read these solutions, you are advised to do two things if you answered the Math question incorrectly: 1. When a specific Strategy is referred to in the solution, study that strategy, which you will find in “Using Critical Thinking Skills in Math Questions” (beginning on page 69). 2. When the solution directs you to the “Math Refresher” (beginning on page 191)—for example, Math Refresher #305—study the 305 Math principle to get a clear idea of the Math operation that was necessary for you to know in order to answer the question correctly.

1.


2.


(Use Strategy 2: Translate from words to algebra.)

Given: 8 people divide a cash prize equally

Let g number of games the team played 28 number of games Bobby watched 2 g number of games Tommy watched 3

(Use Strategy 2: Translate from words to algebra.) From 1 we get: 1 Each person receives of the total prize 8 2 1 2 people receive of the prize 8 4

We are given 2 g 28 3

1

2 3

To change 3 to a percent we multiply by 100.

3 Multiplying 1 by , we get 2

1

1 100 100 4 4

3 2 3 g 28 2 3 2 g 42

25% (Math Refresher 200 and 106)

Only Choice E satisfies this relationship. (Math Refresher 200, 422, and 426)

642

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3.


(Use Strategy 5: Sum of values Average Total number of values

(Use Strategy 10: Know how to use units.) 90 laps We are given his rate is 6 hours

Sum of values We know Average Total number of values 3

90 laps

90 laps 1h our 6 ho

urs 60 minutes 360 minutes

Let x be the first test score y be the second test score z be the third test score

1 lap per minute (Answer) 4

4

xyz 85 3

1/x 1/() x 4 x3/4 1/(16 )3 1/(2)3 1/8

3/4

Choice C is correct. x

3/4

3

Multiply 7 by 3. We get xyz 3(85) 3 3

Choice E is correct. The graph y 2 x 4 is a straight line such that when x 0, y 4 and when y 0, 2 x 4 0 and thus x 2. So we look for a line that cuts the y-axis (vertical axis where x 0) at y 4, and cuts the x-axis (horizontal axis where y 0) at x 2.

xy 85 2 xy 2(85) 2 2

170 x y

100 3 Thus 9 hundredths. 10 3 10

2

9


225 170 z 85 z (Math Refresher 601, 431, and 406) 9.

Choice A is correct. (Use Strategy 11: Use new definitions carefully.) Given: x ⱓ y 3 xy y 0 xⱓy3

1 2 3

3 3 xy 0 xy

4

Noting 2 , we divide 4 by y

Choice B is correct. Given: Paul’s average on 3 tests 85 Paul’s average on first 2 tests 85

10


2

8.


Checking the choices, we find only Choice D has a18b12 and must be correct. Note: We did not have to calculate 36!

Choice C is correct. (Use Strategy 17: Use the given information effectively.)

9

Multiply 9 by 2, we get

[(3a3b2)3]2 (3a3b2)6 36a18b12

7.

8

Substituting 2 , 4 and 5 into 3 , we have

Choice D is correct. (Use Strategy 17: Use the given information effectively.)


255 x y z


7

(Use Strategy 13: Find unknowns by multiplication.)


4 5 6

Substituting 1 , 4 , 5 and 6 into 3 , we have


1 2

0 xy y y 0x (Math Refresher 431 and 406)

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10.


13.


(Use Strategy 3: The whole equals the sum of its parts.)

(Use Strategy 2: Translate from words to algebra.)

From the given diagram, it is clear that

The ratio of Sue’s age to Bob’s age is 3 to 7, becomes

z 2w 180

1

3 Sue’s age (S) 7 Bob’s age (B)

Since the sum of the measures of the angles of a triangle is 180, then x y z 180

3 S 7 B

or

2

The ratio of Sue’s age to Joe’s age is 4 to 9, becomes

(Use Strategy 13: Find unknowns by subtracting equations.)

S 4 J 9

Subtracting 2 from 1 , or

2w (x y) 0 2w x y

2

Cross multiplying 1 , we have 7S 3B

3

or

Using 3 , we calculate the unknown expression, w x y w 2w 3w

7S B 3

3

Cross multiplying 2 , we have 9S 4J or

(Math Refresher 501, 505, and 406)

9S J 4

4

We need the ratio of Bob’s age to Joe’s age. 11.

1


5


(Use Strategy 11: Use new definitions carefully.)

Bob’s age Joe’s age

All choices must be evaluated using the definition. Choice A, 934432, would be assigned 6 3 4 13 points, while the other choices all receive fewer than 13 points.

7S 3 9S 4

7S 9S 3 4 7S 4 3 9S

(Logical Reasoning)

Bob’s age 28 Joe’s age 27 (Math Refresher 200, 120, and 112)

12.

Choice D is correct. Given: A certain number has 13 points. (Use Strategy 11: Use new definitions carefully.) From the chart, the only ways to accumulate 13 points are: 643 3334 I. 33 is not in the number is always true. II. 34 and 43 are both in the number is not true in III. 43 is in the number is always true.

14.


1 2

(Use Strategy 17: Use the given information effectively.) 1

2

Given: Area of circle 9a2p 2 Two sides of square are tangent to the circle We know that area of a circle p (radius)2 Substituting 1 into 3 , we have

3

Thus, I and III are always true. (Logical Reasoning)

9a2p 2 p(radius)2

2

4

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SAT PRACTICE TEST 1 – SECTION 8 ANSWERS • 645 15.

Circumference of circle


6 7p (since there are 6 arcs) We know circumference 2p r

6 7

Using 6 and 7 , we get

Given: BAF 14p ABCDEF is equilateral

1 2

From 2 we know that all 6 sides are From 3 we know that all 6 arcs are equal. From 1 and 4 we find

3 4

AB BC CD DE EF FA 7p

5

2p r 6 7p 2p r 42p 2r 42 We know diameter 2 radius So diameter 42

8 9


Choice B is correct. f(x) ax so f(x y) a xy a xy a xa y f(x)f(y)

(Use Strategy 3: The whole equals the sum of its parts.)


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Explanatory Answers for Practice Test 1 (continued) Section 9: Critical Reading As you read these Explanatory Answers, you are advised to refer to “Using Critical Thinking Skills in Verbal Questions” (beginning on page 118) whenever a specific Strategy is referred to in the answer. Of particular importance are the following Master Verbal Strategies: Sentence Completion Master Strategy 1—page 118. Sentence Completion Master Strategy 2—page 119. Reading Comprehension Master Strategy 2—page 136. Note: All Reading questions use Reading Comprehension Strategies 1, 2, and 3 (pp. 133–138) as well as other strategies indicated.

1.

Choice E is correct. See Sentence Completion Strategy 2. Examine the first word of each choice. Choice (B) relegates (meaning to banish or to assign to a lower position) . . and Choice (C) accumulates . . do not make sense since we do not say that a sense of fairness relegates or accumulates. Now consider the other choices. Choice (E) dictates . . varies, is the only choice that makes sentence sense.

2.

Choice A is correct. See Sentence Completion Strategy 1. The typist’s inconsistency is obvious in the manner in which she typed the five letters. Choices B, C, D, and E are incorrect because they do not make good sense in the sentence.

3.

Choice B is correct. See Sentence Completion Strategy 2. Let us first examine the first words of each choice. We can then eliminate Choice (C) remarks . . and Choice (E) conferences . . because an outstanding publisher’s being able to make occasional remarks or occasional conferences does not make good sense. Now we go on to the three remaining choices. When you fill in the two blanks of Choice A and of Choice D, the sentence does not make sense. So these two choices are also incorrect. Filling in the two blanks of Choice B makes the sentence meaningful. 646

4.

Choice B is correct. See Sentence Completion Strategy 1 and 4. Try each choice being aware that “since” is a result indicator. Their married life was not smooth and content.

5.

Choice B is correct. See Sentence Completion Strategy 1 and 4. Try each choice, being aware that “because” is a result indicator. This happened because of his careless, indifferent driving.

6.

Choice D is correct. See Sentence Completion Strategy 1. Try each choice. Parables are stories or fables that illustrate a moral or ethical point while relating a simple incident.

7.

Choice D is correct. Line 1 (“To the world when it was half a thousand years younger . . .”) indicates that the author is describing the world roughly five hundred years ago. Choice D—A.D. 1455—is therefore the closest date. Although Choice C is also in the Middle Ages, it is almost a thousand years ago. So it is an incorrect choice. Choices A, B, and E are obviously incorrect choices.

8.

Choice A is correct. We can see that “with greater avidity” is an adverbial phrase telling the reader how “honors and riches” were enjoyed and desired. See lines 14–17: “We, at the present day . . . formerly

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with conditions that may make the Middle Ages seem better than today. Choice C is incorrect because nowhere in the passage is intelligence mentioned or implied. Choice D is incorrect because the third paragraph indicates that, far from being subdued, people went about their lives with a great deal of show and pageantry.

enjoyed.” The reader thus learns that even simple pleasures such as a glass of wine were more keenly enjoyed then. Choices B, C, D, and E are incorrect because the passage does not state or imply that “with greater avidity” means “with greater sadness or terror or silence or disappointment. See also Reading Comprehension Strategy 5. 9.

Choice B is not true—therefore it is the correct choice. See lines 36–38: “The contrast between silence and sound . . . than it is in our lives.” The next sentence states that the modern town hardly knows silence. These two sentences together imply that the typical town of the Middle Ages did have periods of silence.

12.

Choice A is incorrect because the author stops short of outright despair in the last sentence of the first paragraph by tempering the outbursts of the Renaissance scholar with the milder “our times are out of joint.” Choices B and E are incorrect because there is no positive feeling expressed in the first paragraph. Choice C is incorrect because there is no feeling of attraction toward an earlier age. Choice D is correct because the negative feeling is not quite full-bodied.

13.

Choice A is correct. There is no mention of energy sources at any point in the selection. Therefore this answer is correct. Choices B, C, D, and E are mentioned in paragraph 2.

14.

Choice B is correct. The positive outlook of the words “trend is not destiny” is best exemplified by Choice B, which implies that man can improve his situation. The other statements are negative or pessimistic pronouncements.

15.

Choice A is correct. The author cites Choices B, C, D, and E in paragraph 5 as examples of renewed public awareness. The reference to the president’s increase in the military budget does not indicate evidence of the public’s insight regarding a danger.

16.

Choice B is correct. Choices A and C are incorrect because the author is consistently expressing optimism in man’s ability to learn from past mistakes. Choice B is the correct answer. Accordingly, Choice D contradicts the realistic tone of the essay. Choice E is not at all characteristic of the writer’s attitude.

17.

Choice C is correct. See lines 13–14 and lines 56–59. Note that the author of Passage B states that if present trends continue, the gap in living standards between the rich and the poor will lead to acts of desperation, including the use of nuclear weapons.

18.

Choice A is correct. See lines 73–78. Note that Choice B is incorrect; see lines 41–46 and the descriptions in the rest of Passage A. Choice C is incorrect; see lines 82–84. Choice E is incorrect; see lines 86–88.

19.

Choice E is correct. See lines 73–90 and lines 41–46 and throughout Passage A. Note that Choice A is incorrect; see lines 88–90.

Choice A is true—therefore an incorrect choice. See lines 30–31: “A medieval town . . . in extensive suburbs of factories and villas.” Choice C is true—therefore an incorrect choice. See lines 32–33: “. . . it [a medieval town] stood forth . . . with innumerable turrets.” Choice D is true—therefore an incorrect choice. See line 35: “. . . the lofty mass of the churches always remained dominant.” Choice E is true—therefore an incorrect choice. See lines 33–34: “However tall . . . in the aspect of the town.” 10.

11.

Choice C is correct. Throughout Passage A, the author is indicating the strong, rough, uncontrolled forces that pervaded the period. See, for example, the following references. Lines 9–10: “Misfortunes and poverty were more afflicting than at present.” Lines 18–19: “Then, again, all things in life . . . cruel publicity.” Lines 24–26: “Executions . . . songs and music.” Therefore, Choice C is correct. Choice A is incorrect because the passage speaks of joys as well as miseries. See lines 14–17: “We, at the present day . . . formerly enjoyed.” Choice B is incorrect for this reason: Although the author contrasts town and country, he gives no indication as to which was dominant in that society. Therefore, Choice B is incorrect. Choice D is incorrect. The author contrasts how it felt to be rich or poor, but he does not indicate that the rich mistreated the poor. Choice E is incorrect because the pious nature of the people in the Middle Ages is only one of the many elements discussed in the passage. Choice E is correct. See lines 4–6: “All experience . . . pain of child-life.” Throughout the passage, this theme is illustrated with specific examples. Choices A and B are incorrect because they are one-sided. In the passage, many conditions that may make the Middle Ages seem worse than today are matched

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Explanatory Answers for Practice Test 1 (continued) Section 10: Writing For further practice and information, please refer to Grammar and Usage Refresher starting on p. 461.

1. Choice D is correct. Choices A, B, and C are incor-

7.

rect because they lack parallelism. Note that the infinitive phrase “to write poems” should balance with the infinitive phrase “to study the habits.” Choice D, which does have the parallelism required, is correct. Choice E is too wordy. 2. Choice B is correct. This question is concerned

with the correct position of the gerund phrase “By studying.” Choice A is incorrect because “grades” have been doing the “studying” with such sentence structure. Choices C, D and E are incorrect for the same reason. Choice B is correct since “she” is obviously the one who is doing the “studying.”

Choice C is correct. A misplaced modifier may create a very embarrassing situation—so we can observe in the original sentence. We certainly don’t want the fiancé wearing a sheer blouse. Such a blouse clearly belongs on the female. Choices A and D are, therefore, incorrect. Choice B is incorrect because it may appear that the concert is wearing the sheer blouse. Choice C is, of course, correct. Choice E is not acceptable because (1) the phrase “wearing a sheer blouse” is a “squinting” modifier, and (2) the sentence would be inappropriately poetic.

8. Choice D is correct. We are looking for balanced

construction in this question. Note that the correct Choice D gives us a balanced infinitive construction. “to advise,” “(to) transmit”, and “(to) supervise.” None of the other choices offers this balanced construction.

3. Choice D is correct. Choice A is incorrect because

of the improper omission of the demonstrative pronoun “those:” Choices B and C are incorrect for the same reason. Choice D is correct. Choice E is incorrect because we must bring out the comparison with another city.

9. Choice A is correct. Choices B and C are incorrect

because Frazier did not “own” the decision—it was rendered by the judges and the referee. Choice D is too roundabout. Choice E changes the meaning of the original sentence—and it is too roundabout.

4. Choice C is correct. Parallelism is the important

consideration here. Choice C is correct as the only choice that fulfills the requirements of parallel structure. 5. Choice D is correct. The expression “one another”

10.

Choice C is correct. Choices A, B, and E suffer from incomplete comparison. The conjunction (a second “as”) is required to complete the comparison: “This test was as hard . . . as the one I took last week.” Choice D is incorrect because the conjunction “so” should be used in a negative construction: “This test was not so hard . . .” Choice C is correct because it completes the comparison.

11.

Choice E is correct. Choice A is incorrect because the plane and not JFK Airport carried few passen-

refers to three or more; “each other” refers to two only. Therefore, Choices A and B are incorrect and Choice D is correct. Choice C is awkward. Choice E changes the meaning of the original sentence. 6. Choice E is correct. The past contrary-to-fact con-

ditional form is “had seen.” Therefore, Choices A, B, C, and D are all incorrect. Choice E is correct. Moreover, Choice C has the wrong tense and the wrong tense sequence. 648

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gers. Choice B is incorrect because there is a lack of agreement in the verb tenses. Also the active voice should be used. See correct Choice E. Choice C does not include a reference to JFK Airport which is necessary to the meaning of the original sentence. Choice D is ambiguous. E is correct. 12.

Choice C is correct. Choice A is incorrect because the word “go” is needed after the word “to” (otherwise the sentence means “I wanted to gone”). Choice B also requires the word “go” after “to.” Choice C is correct. In Choice D, the word “although” changes the original sentence to a fragment. Choice E requires the words “to go” after “wanted.”

13.

Choice D is correct. Choices A and B are incorrect because “Either” should be placed before “today.” Choice C is too wordy. Choice D is correct. Choice E is awkward.

14.

Choice C is correct. Choice A is incorrect because “which” should be used to refer to a noun or pronoun and not a clause, as it is used here. In Choice B, there is a lack of agreement in the verb tenses. Choice C is correct. Choice D is awkward. Choice E is a complete sentence, making the original a run-on sentence.

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What You Must Do Now to Raise Your SAT Score 1.

2.

5) Listen to people who speak well. Tune in to worthwhile TV programs also.

a) Follow the directions on p. 607 to determine your scaled score for the SAT Test you’ve just taken. These results will give you a good idea about whether or not you ought to study hard in order to achieve a certain score on the actual SAT. b) Using your correct answer count as a basis, indicate for yourself your areas of strength and weakness as revealed by the “Self-Appraisal Chart” on page 616.

6) Use the dictionary frequently and extensively—at home, on the bus, at work, etc. 7) Play word games—for example, crossword puzzles, anagrams, and Scrabble. Another game is to compose your own Sentence Completion questions. Try them on your friends.

Eliminate your weaknesses in each of the SAT test areas (as revealed in the “Self-Appraisal Chart”) by taking the following Giant Steps toward SAT success:

Math Part Giant Step 3

Critical Reading Part

Make good use of the Math Strategies that begin on page 69. Read again the solutions for each Math question that you answered incorrectly. Refer to the Math Strategy that applies to each of your incorrect answers. Learn each of these Math Strategies thoroughly. We repeat that these strategies are crucial if you want to raise your SAT Math score substantially.

Giant Step 1 Take advantage of the Critical Reading Strategies that begin on page 118. Read again the Explanatory Answer for each of the Critical Reading questions that you got wrong. Refer to the Critical Reading Strategy that applies to each of your incorrect answers. Learn each of these Critical Reading Strategies thoroughly. These strategies are crucial if you want to raise your SAT Verbal score substantially.

Giant Step 4 You may want to take The 101 Most Important Basic Skills Math Questions You Need to Know How to Solve test on page 29 and follow the directions after the test for a basic math skills diagnosis. For each Math question that you got wrong in the test, note the reference to the Math Refresher section on page 48. This reference will explain clearly the mathematical principle involved in the solution of the question you answered incorrectly. Learn that particular mathematical principle thoroughly.

Giant Step 2 You can improve your vocabulary by doing the following: 1) Study the SAT 3,400-Word List beginning on page 363. 2) Take the 100 SAT-type “tough word” Vocabulary Tests beginning on page 415. 3) Study “Word Building with Roots, Prefixes, and Suffixes,” beginning on page 352. 4) Read as widely as possible—not only novels. Nonfiction is important too . . . and don’t forget to read newspapers and magazines.

650

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For Both the Math and Critical Reading Parts Giant Step 5 You may want to take the Strategy Diagnostic Test on page 1 to assess whether you’re using the best strategies for the questions.

For the Writing Part Giant Step 6 Take a look at Part 9—The SAT Writing Test which describes the various item types in the Writing Section and sample questions with answers and explanations. Also make use of the Grammar Refresher—Part 8. 3.

After you have done some of the tasks you have been advised to do in the suggestions above, proceed to Practice Test 2, beginning on page 652. After taking Practice Test 2, concentrate on the weaknesses that still remain.

4.

Continue the foregoing procedures for Practice Tests 3, 4, and 5. If you do the job right and follow the steps listed above, you are likely to raise your SAT score on each of the Verbal, Math, and Writing parts of the test 150 points—maybe 200 points—and even more. I am the master of my fate; I am the captain of my soul. —From the poem “Invictus” by William Ernest Henley

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Answer Sheet for Practice Test 2

SECTION 1 Begin your essay on this page. If you need more space, continue on the next page. Do not write outside of the essay box.

Continue on the next page if necessary. 652

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Continuation of ESSAY Section 1 from previous page. Write below only if you need more space.

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SECTION

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CAUTION

Use the answer spaces in the grids below for Section 2 or Section 3 only if you are told to do so in your test book. ONLY ANSWERS ENTERED IN THE CIRCLES IN EACH GRID WILL BE SCORED. YOU WILL NOT RECEIVE CREDIT FOR ANYTHING WRITTEN IN THE BOXES ABOVE THE CIRCLES.


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SECTION

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CAUTION



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CAUTION



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SECTION

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9 A 10 A

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19

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29

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39

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SAT PRACTICE TEST 2

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Page 659

SECTION 1

Time: 25 Minutes—Turn to page 652 of your answer sheet to write your ESSAY.

The purpose of the essay is to have you show how well you can express and develop your ideas. You should develop your point of view, logically and clearly present your ideas, and use language accurately. You should write your essay on the lines provided on your answer sheet. You should not write on any other paper. You will have enough space if you write on every line and if you keep your handwriting to a reasonable size. Make sure that your handwriting is legible to other readers. You will have 25 minutes to write an essay on the assignment below. Do not write on any other topic. If you do so, you will receive a score of 0. Think carefully about the issue presented in the following excerpt and the assignment below.

“It has been often said that rapid technological change requires us to change our morals, customs, and institutions. This observation is believable only if we assume that humanity was made for the machine, not the machine for humanity. If anything, technological progress makes our sense of tradition more necessary than ever. Maintaining traditions is not (or need not be) merely a resistance to change, but a positive attachment to some par ticular way of life and the community that embodies it.” —Adapted from Karl Jahn, “Tradition and Progress”

Assignment: In the above excerpt, Jahn argues that we do not have to change our traditions to keep pace with technological changes. To what extent do you agree or disagree with his position? Support your position with reasons and examples from your own experience, reading, and observations. DO NOT WRITE YOUR ESSAY IN YOUR TEST BOOK. You will receive credit only for what you write on your answer sheet. BEGIN WRITING YOUR ESSAY ON PAGE 652 OF THE ANSWER SHEET.

If you finish before time is called, you may check your work on this section only. Do not turn to any other section in the test. 659

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Notes:




1. Given that 500w 3 700, find the value of w.

2.

5 (A) 21

3y If 7, then y y (A) (B) (C) (D)

4 3 2 1 1 (E) 2

(B) 2 11 (C) 5 21 (D) 5 (E) 7


660

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Page 661

SAT PRACTICE TEST 2 – SECTION 2 • 661 3. The positive integer x is a multiple of 9 and also a

multiple of 12. The smallest possible value of x is (A) (B) (C) (D) (E)

3 12 21 36 72

Note: Figure is not drawn to scale. 5.

In the figure above, squares I, II, and III are situated along the x-axis as shown. Find the area of square II. (A) (B) (C) (D) (E)

4.

Find (r s)(t s) (s r)(s t) for all numbers r, s, and t. (A) (B) (C) (D) (E)

0 2 2rt 2(s r)(t s) 2(r s)(t s)

6.

16 25 49 100 121

A certain cup holds 100 grams of butter. If a cake requires 75 grams of butter and a pie requires 225 grams of butter, then 4 cups of butter is not enough for any of the following except (A) (B) (C) (D) (E)

6 cakes 2 pies 3 cakes and 1 pie 2 cakes and 2 pies 2 cakes and 1 pie


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Page 662



In the rectangular coordinate system above, which of the following is true about line ᐉ? I. the slope is 1 II. the distance of point (0,a) to point (a,0) is equal to a2 III. the acute angle that the line ᐉ makes with the x-axis is 45° (A) (B) (C) (D) (E)

If the sum of the four terms in each of the diagonal rows is the same, then A (A) (B) (C) (D) (E)

4 5 6 7 8

I only II only III only II and III only I, II, and III

a 8.

9.

b –2

0

+3

c

In the above number line, a, b, and c are real numbers. Which is true? (A) (B) (C) (D) (E)

b -1 b 2 c c b a a b

10. The two dials shown above operate simultaneously

in the following manner. The hand in A turns counterclockwise while the hand in B turns clockwise. The hand of A moves to 9 at exactly the same moment that the hand of B moves to 3. Then the hand of A moves to 6 at exactly the same moment that the hand of B moves to 6, and so on. If each hand starts at 12, where will each hand be at the end of 17 moves? (A) (B) (C) (D) (E)

Both at 12 Both at 9 A at 3 and B at 12 A at 3 and B at 9 A at 9 and B at 3


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Page 663

SAT PRACTICE TEST 2 – SECTION 2 • 663 11. Given that w 7r 6r 5r 4r 3r, which of

the terms listed below may be added to w so that the resulting sum will be divisible by 7 for every positive integer r? (A) (B) (C) (D) (E)

7r 6r 5r 4r 3r

13. Which of the following is always true for a,b,x,y

real? I. (a x )y a xy II. a x y a xa y III. (ab)x a xb x (A) (B) (C) (D) (E)

I only II only III only I and II only I, II, and III

12. S is a set of positive, odd, whole numbers in which

14. A painter earns $10 an hour for all hours spent on

no two numbers are the same. If the sum of all of its members is 64, then what is the maximum number of members that S can have?

a job. For a certain job, he worked from 7:00 A.M. until 5:00 P.M. on Monday, Tuesday, and Thursday and from 1:00 P.M. until 7:00 P.M. on Wednesday, Friday, and Saturday. How much did he earn for the entire job?

(A) 10 (B) 13 (C) 6 (D) 8 (E) 7

(A) (B) (C) (D) (E)

$420 $450 $480 $510 $540


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Page 664


17.

a1 where a and b are positive inteb1 gers and b 1, which of the following is largest?

If

a

(A) (B) (C) (D) (E)

b

2 3 3 3 3 5 4 5 5 3

Note: Figure is not drawn to scale. 15. Given RST above, what is the value of b?

(A) (B) (C) (D) (E)

50 40 30 20 10

Question 16

18. In RST above, RS and ST have lengths equal to the

same integer. All of the following could be the area of triangle RST except

16. John works for 5 days. His daily earnings are dis-

played on the above graph. If John earned $35 on the sixth day, what would be the closest difference between the median and the mode of the wages during the six days? (A) (B) (C) (D) (E)

$5.5 $6.5 $7.5 $8.5 $9.5

1 (A) 2 (B) 2 1 (C) 4 2 1 (D) 12 2 (E) 20


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SAT PRACTICE TEST 2 – SECTION 2 • 665 19. A rectangular solid has dimensions of 2 feet

20. A circle is inscribed in a square. If the perimeter of

2 feet 1 foot. If it is sliced in small cubes, each of edge .1 foot, what is the maximum number of such cubes that can be formed? (A) (B) (C) (D) (E)

40 500 1,000 2,000 4,000

the square is 40, what is the area of the circle? (A) (B) (C) (D) (E)

100p 50p 40p 25p 5p



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Notes:



1.


If 3 is added to a number and this sum is divided by 4, the result is 6. What is the number? (A) (B) (C) (D) (E)

2.

5 7 12 21 27

3 4 Given that x , which of the following 4 5 is a possible value of x? 7 (A) 16 13 (B) 20 31 (C) 40 16 (D) 20 6 (E) 7


666

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3.

If the perimeter of a square is 20 meters, how many square meters are contained in its area? (A) (B) (C) (D) (E)

4.

100 25 20 10 5

Given that 80 a 32 b, find the value of b a. (A) (B) (C) (D) (E)

5.

112 48 2.5 48 112

If x is a positive integer, which of the following must be an even integer? (A) (B) (C) (D) (E)

6.

x2 2x 1 3x 1 x2 x 1 x2 x 2

If ax r and by r 1, then which of the following is a correct expression for x? by 1 (A) a by 1 (B) a by r (C) a (D) by ar (E) ab ry


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7.

Container A holds twice as much as container B, and container C holds as much as A and B put together. If we start with A and B full, and C empty, and pour half the contents of A and a third of the contents of B into container C, what fraction of C ’s capacity will be filled? 5

(A) /6

8.

What is the diameter of a wheel which, when rotating at a speed of 10 revolutions per minute, takes 12 seconds to travel 16 feet? (A) 4p feet 4 (B) feet p

(B) 4/9

(C) 8p feet

(C) 5/12

8 (D) feet p 16 (E) feet p

(D) 7/12 (E) 7/18


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Directions: For Student-Produced Response questions 9–18, use the grids at the bottom of the answer sheet page on which you have answered questions 1–8. Each of the remaining 10 questions requires you to solve the problem and enter your answer by marking the circles in the special grid, as shown in the examples below. You may use any available space for scratchwork. 7 Answer: or 7/12 12

Grid in result.

➝

7

1

/

2

/ .

.

.

.

0

0

0

➝

➝

Fraction line

1

.

1

2

.

/

/

.

.

Decimal point

.

0

0

1

1

1

1

2

2

2

1

1

2

2

2

3

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

4

4

5

5

5

5

5

5

5

6

6

6

6

6

6

6

7

7

7

7

7

7

7

8

8

8

8

8

8

8

8

9

9

9

9

9

9

9

9

6

/

.

.

0

0

2

0

/

1

1

.

2

.

0

1

/

/

.

0 1

1

2

2

3

3

3

4

4

4

.

.

0

0

1

1

2

2

2

3

3

3

3

4

4


●


●



●


2 Acceptable ways to grid .6666 … 3

●


●

●

No question has a negative answer. 1 Mixed numbers such as 2 must be gridded as 2 2.5 or 5/2. (If

2

1 /

/

2


1 21 interpreted as , not 2 .) 2 2 9.

2

5

➝



Answer: 2.5

5 3 If of a number is 3 less than of the number, 8 4 what is the number?

●

2

/

3

.

/ .

1

6 /

6

6

.

/

6 /

6

7

/

.

.

.

.

.

.

.

.

.

0

0

0

0

0

0

0

0

0

1

1

1

1

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

2

2

3

3

3

3

3

3

3

3

2 3

3

3

4

4

4

4

4

4

4

4

4

4

4

4

5

5

5

5

5

5

5

5

5

5

5

5

6

6

6

6

6

10.

Let

6

6

represent the greatest even integer

less than n that divides n, for any positive integer n. For example,

12. Find the value of


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11.

If m 94 and n 6, then find the value of 23m 23n.

12.

A horizontal line has a length of 100 yards. A vertical line is drawn at one of its ends. If lines are drawn every ten yards thereafter, until the other end is reached, how many vertical lines are finally drawn?

16.

Given the circle, above, with center P, what is the length of its radius?

17.

A lawn covers 108.6 square feet. Russ mowed all 2 of the lawn in three evenings. He mowed of 9 of the lawn during the first evening. He mowed twice that amount on the second evening. On the third and final evening he mowed the remaining lawn. How many square feet were mowed the third evening?

Note: Figure not drawn to scale 13.

In the circle above with center O, diameter AC, and AB BC, find the value of x y.

14.

In a certain class containing 60 students, the average (arithmetic mean) age is 20. In another class containing 20 students, the average age is 40. Find the average age of all 80 students.

18. 15.

In the addition problem shown below, if 䊐 is a constant, what must 䊐 equal in order for the answer to be correct?

䊐 6

䊐 15

If 9 people are standing in a straight line in a circle, what is the smallest number of people who must move so that all 9 will be standing on the circumference of a circle?

1

䊐 9

䊐


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SECTION 4 Time: 25 Minutes—Turn to Section 4 (page 655) of your answer sheet to answer the questions in this section. 24 Questions Directions: For each question in this section, select the best answer from among the choices given and fill in the corresponding circle on the answer sheet. 3. Because the people of India were

under ––––––––––––– British rule, many went over to the Japanese side during World War II.


(A) (B) (C) (D) (E)


4.


1.

C

D

5.

emotion opportunity exposure competition creativity

6.

capable . . limited tantamount . . tremendous collegiate . . remarkable scholarly . . profound active . . carefree

rational precarious payable insufficient incomprehensible

Maggie was quite –––––––––– about having her husband remove his shoes before the stepped into the living room; yet the rest of the apartment was very whenever I visited them. ––––––––– (A) (B) (C) (D) (E)

He is one of the most –––––––––– professors that I have ever had, with a –––––––––– knowledge of his subject and a thoroughness in his teaching. (A) (B) (C) (D) (E)

The author told the publisher that the royalty payment specified in the contract was ––––––––––––– because the research costs, including traveling for writing the book, were far more than the royalties projected for a year. (A) (B) (C) (D) (E)

Though he was a highly skilled computer programmer, he had little or no ––––––––––––– in designing educational software. (A) (B) (C) (D) (E)

2.

B

employed deported educated abused satisfied

indifferent . . comfortable perplexed . . weird firm . . disorderly considerate . . modern humorous . . attractive

Those who were invited to Peter’s party had to come dressed in –––––––––– clothes, thus convincing all the guests of his ––––––––– inclination. (A) (B) (C) (D) (E)

sonorous . . imaginative tawdry . . humble raucous . . peaceloving tattered . . nightmarish old-fashioned . . nostalgic


671

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7.

Her devotion to music ––––––––––––– his own interest in an art he had once loved as a child. (A) (B) (C) (D) (E)

belied revived defiled reviled exiled

8.

President Anwar el-Sadat of Egypt, disregarding criticism in the Arab world and in his own –––––––––– government, ––––––– accepted Prime Minister Menachem Begin’s invitation to visit Israel in order to address the Israeli Knesset. (A) (B) (C) (D) (E)

categorical . . previously blemished . . stiffly charismatic . . meticulously acrimonious . . formally malignant . . plaintively


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Each passage below is followed by questions based on its content. Answer the questions on the basis of what is stated or implied in each passage and in any introductory material that may be provided.



A legendary island in the Atlantic Ocean beyond the Pillars of Hercules was first mentioned by Plato in the Timaeus. Atlantis was a fabulously beautiful and prosperous land, the seat of an empire nine thousand years before Solon. Its 5 inhabitants overran part of Europe and Africa, Athens alone being able to defy them. Because of the impiety of its people, the island was destroyed by an earthquake and inundation. The legend may have existed before Plato and may have sprung from the concept of Homer’s Elysium. 10 The possibility that such an island once existed has caused much speculation, resulting in a theor y that preColumbian civilizations in America were established by colonists from the lost island.

Lithography is the art of drawing with a greasy substance, usually crayon, on a stone, metal, or paper surface, and then printing. It is based on the fact that grease attracts grease and is repelled by water. It is the most direct of all 5 the graphic arts, for in practicing it the artist first sees the exact value of each line that he draws and then has his drawing reproduced so accurately that it may truly be said to have been multiplied. In making either an etching, a process in which a drawing is engraved on a metal plate 10 through a thin film of wax, or a woodblock, in which the drawing is carved in wood, the artist must wait for a print to estimate his work fairly. When a lithograph is made, the artist’s drawing grows in definite values under his eyes and he can make changes in it as he works.

9. According to the passage, we may most safely con-

11. A great advantage of lithography as a means of

1

1

clude that the inhabitants of Atlantis

reproducing drawings is that it

(A) (B) (C) (D) (E)

(A) (B) (C) (D) (E)

were known personally to Homer were ruled by Plato were a religious and superstitious people used the name Columbia for America left no recorded evidence of their existence

10. According to the legend, Atlantis was destroyed

is quicker and neater than other methods gives faithful reproductions requires a metal plate requires no special materials is less expensive than other methods

12. Many artists like to use lithography to reproduce

because the inhabitants

their drawings because they

(A) (B) (C) (D) (E)

(A) know in advance the value of each picture (B) often get unexpected results (C) get higher prices for lithographs than for etchings (D) can get clearer enlargements (E) can make alterations and corrections

failed to obtain an adequate food supply failed to conquer Greece failed to respect their gods believed in Homer’s Elysium had become too prosperous


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One may readily describe four specific forms of the same general contradiction. Occupationally, the work force 45

The following passage discusses advanced technological institutions and their relation to the work force with social implications.

5

10

15

20

25

30

A second major hypothesis would argue that the most important dimension of advanced technological institutions is the social one; that is, the institutions are agencies of highly centralized and intensive social control. Technology conquers nature, as the saying goes. But to do so it must first conquer man. More precisely, it demands a very high degree of control over the training, mobility, and skills of the work force. The absence (or decline) of direct controls or of coercion should not serve to obscure from our view the reality and intensity of the social controls which are employed (such as the internalized belief in equality of opportunity, indebtedness through credit, advertising, selective service channeling, and so on). Advanced technology has created a vast increase in occupational specialties, many of them requiring many, many years of highly specialized training. It must motivate this training. It has made ever more complex and “rational” the ways in which these occupational specialties are combined in our economic and social life. It must win passivity and obedience to this complex activity. Formerly, technical rationality had been employed only to organize the production of rather simple physical objects, for example, aerial bombs. Now technical rationality is increasingly employed to organize all of the processes necessary to the utilization of physical objects, such as bombing systems, maintenance, intelligence and supply systems. For this reason it seems a mistake to argue that we are in a “post-industrial” age, a concept favored by the laissez innover school. On the contrary, the rapid spread of technical rationality into organizational and economic life and, hence, into social life is more aptly described as a second and much more intensive phase of the industrial revolution. One might reasonably suspect that it will create analogous social problems.

50

55

60

65

70

75

80

Accordingly, a third major hypothesis would argue that 35 there are very profound social antagonisms or contradic-

tions not less sharp or fundamental than those ascribed by Marx to the development of nineteenth-century industrial society. The general form of the contradictions might be described as follows: a society characterized by the employ40 ment of advanced technology requires an ever more socially disciplined population, yet retains an ever declining capacity to enforce the required discipline.

85

90

must be over-trained and under-utilized. Here, again, an analogy to classical industrial practice serves to shorten and simplify the explanation. I have in mind the assembly line. As a device in the organization of the work process the assembly line is valuable mainly in that it gives management a high degree of control over the pace of the work and, more to the point in the present case, it divides the work process into units so simple that the quality of the work performed is readily predictable. That is, since each operation uses only a small fraction of a worker’s skill, there is a very great likelihood that the operation will be performed in a minimally acceptable way. Alternately, if each operation taxed the worker’s skill there would be frequent errors in the operation, frequent disturbance of the work flow, and a thoroughly unpredictable quality to the end product. The assembly line also introduces standardization in work skills and thus makes for a high degree of interchangeability among the work force. For analogous reasons the work force in advanced technological systems must be relatively over-trained or, what is the same thing, its skills relatively under-used. My impression is that this is no less true now of sociologists than of welders, of engineers than of assemblers. The contradiction emerges when we recognize that technological progress requires a continuous increase in the skill levels of its work force, skill levels which frequently embody a fairly rich scientific and technical training, while at the same time the advance of technical rationality in work organization means that those skills will be less and less fully used. Economically, there is a parallel process at work. It is commonly observed that the work force within technologically advanced organizations is asked to work not less hard but more so. This is particularly true for those with advanced training and skills. Brzezinski’s conjecture that technical specialists undergo continuous retraining is off the mark only in that it assumes such retraining only for a managing elite. To get people to work harder requires growing incentives. Yet the prosperity which is assumed in a technologically advanced society erodes the value of economic incentives (while of course, the values of craftsmanship are “irrational”). Salary and wage increases and the goods they purchase lose their overriding importance once necessities, creature comforts, and an amply supply of luxuries are assured. As if in confirmation of this point, it has been pointed out that among young people one can already observe a radical weakening in the power of such incentives as money, status, and authority.


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13.

The term “technical rationality” is used in conjunction with

18.

(A) there is unwavering worker allegiance to the goals of the institutions (B) there is strict adherence to a laissez innover policy (C) worker and management are in concurrence (D) there is another more intense, industrial revolution (E) the institutions have control over the training, mobility, and skills of the work force

(A) a 20th-century euphemism for the industrial revolution (B) giving credibility to products of simple technology (C) the incorporation of unnecessary skills into economic social living (D) effective organization of production processes (E) safeguarding against technological overacceleration 19. 14.

The author states that advanced technological institutions exercise control by means of (A) (B) (C) (D) (E)

15.

The word “taxed” in line 56 means 20.

fully utilize worker skills fare best under a democratic system necessarily overtrain workers find it unnecessary to enforce discipline are operated by individuals motivated by traditional work incentives

21.

(A) (B) (C) (D) (E)

I and III only I and II only II and III only I, II, and III I only

According to the author, economic incentives (A) are necessary for all but the managerial elite (B) are bigger and better in a society made prosperous by technology (C) cease to have importance beyond a certain level of luxury (D) are impressive only to new members of the work force (E) are impressive to all but the radical young

The value of the assembly line is that it I. minimizes the frequency of error II. allows for interchangeability among the work force III. allows for full utilization of workers’ skills

From the tone of the article, it can be inferred that the author is (A) an eloquent spokesman for technological advancement (B) in favor of increased employee control of industry (C) a social scientist objectively reviewing an industrial trend (D) vehemently opposed to the increase of technology (E) skeptical of the workings of advanced technological institutions

The passage indicates that technologically advanced institutions (A) (B) (C) (D) (E)

17.

The article states that the work force within the framework of a technologically advanced organization is (A) expected to work less hard (B) segregated into levels defined by the degree of technical training (C) familiarized with every process of production (D) expected to work harder (E) isolated by the fact of its specialization

assembly-line work process advertising, selective service channeling, etc. direct and coercive pressures salary incentives authoritarian managerial staffs

(A) a burdensome or excessive demand on the worker (B) a financial obstacle the worker must endure (C) the speed at which the worker must complete the job (D) the efficiency of the worker’s performance on the job (E) the standardization in work skills of the work force 16.

Technologies cannot conquer nature unless

22.

The “managing elite” in lines 80–81 refers to (A) (B) (C) (D) (E)

all the “blue” collar workers the assembly-line workers only the craftsman only the owners of the organizations the top technical specialists


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23.

According to the article, technological progress requires

24.

I. increasing skill levels of work force II. less utilization of work skills III. rich scientific and technical training (A) (B) (C) (D) (E)

I and II only II and III only I and III only III only I, II, and III

The article states that money, status, and authority (A) (B) (C) (D)

will always be powerful work incentives are not powerful incentives for the young are unacceptable to radical workers are incentives that are a throwback to 19th-century industrial society (E) are incentives evolving out of human nature



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SECTION 5 Time: 25 Minutes—Turn to Section 5 (page 655) of your answer sheet to answer the questions in this section. 35 Questions Directions: For each question in this section, select the best answer from among the choices given and fill in the corresponding circle on the answer sheet. 2. So I leave it with all of you: Which came out of the

The following sentences test correctness and effectiveness of expression. Part of each sentence or the entire sentence is underlined; beneath each sentence are five ways of phrasing the underlined material. Choice A repeats the original phrasing; the other four choices are different. If you think the original phrasing produces a better sentence than any of the alternatives, select choice A; if not, select one of the other choices.

open door—the lady or the tiger. (A) the lady or the tiger. (B) the lady or the Tiger! (C) the Tiger or the lady. (D) the Lady or the tiger. (E) the lady or the tiger? 3. The machine is not easy to fool, it isn’ t altogether

foolproof either. (A) it isn’t altogether foolproof either (B) or is it foolproof (C) and it isn’t completely fooled by anyone (D) nor is it entirely foolproof (E) so it isn’t altogether foolproof

In making your selection, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, sentence construction, and punctuation. Your selection should result in the most effective sentence—clear and precise, without awkwardness or ambiguity.

4. The police and agents of the F.B.I. arrested the

ow ner of a M adison A venue art gallery yesterday and charged him with receiving paintings stolen last November.


B

C

D

(A) arrested the owner of a Madison Avenue art gallery yesterday (B) yesterday arrested the owner of a Madison Avenue art gallery (C) arrested the owner yesterday of a Madison Avenue art gallery (D) had the owner of a Madison Avenue art gallery yesterday arrested (E) arranged the arrest yesterday of a Madison Avenue art gallery owner

E

1. Although I know this house and this neighborhood

as well as I know myself, and a lthough m y friend here seem s not hardly to know them at all, nevertheless he has lived here longer than I.

5. At the end of the play about women’s liberation, the

leading lady cautioned the audience not to judge womanhood by the way she dresses. (A) she dresses (B) she dressed (C) they dress (D) they dressed (E) it dresses

(A) and although my friend here seems not hardly to know them at all (B) and even though my friend here seems hardly to know them at all (C) and in spite of the fact that my friend doesn’t hardly seem to know them at all (D) and because my friend here hardly seems to know them at all (E) my friend here seems hardly to know them at all

677

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Page 678

678 • SAT PRACTICE TEST 2 – SECTION 5 6. Go where he may, he is the life of the party.

(A) Go where he may, (B) Where he may go, (C) Wherever he goes, (D) Wherever he may happen to go, (E) Whatever he does,

7. At first we were willing to support him, afterwards

it occurred to us that he ought to provide for him self. (A) (B) (C) (D) (E)

8.

afterwards it occurred to us that that wasn’t the thing to do since but we came to realize that, we came to the conclusion, however, that then we decided that

The statistics were checked and the report was filed. (A) The statistics were checked and the report was filed. (B) The statistics and the report were checked and filed. (C) The statistics were checked and the report filed. (D) The statistics and the report were checked and filed respectively. (E) Only after the statistics were checked was the report filed.

9. Dick was awarded a medal for bravery on account

he risked his life to save the drowning child. (A) on account he risked his life (B) being that he risked his life (C) when he risked his life (D) the reason being on account of his risking his life (E) since he had risked his life

10. The teacher asked the newly admitted student

which was the country that she came from. (A) which was the country that she came from. (B) from which country she had come from. (C) the origin of the country she had come from. (D) which country have you come from? (E) which country she was from. 11. If Jack would have listened to his wife, he would not

have bought those worthless stocks. (A) (B) (C) (D) (E)

would have listened to his wife would listen to his wife had listened to his wife listened to what his wife had said would have listened to his wife’s advice

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The following sentences test your ability to recognize grammar and usage errors. Each sentence contains either a single error or no error at all. No sentence contains more than one error. The error, if there is one, is underlined and lettered. If the sentence contains an error, select the one underlined part that must be changed to make the sentence correct. If the sentence is correct, select choice E. In choosing answers, follow the requirements of standard written English. Example: The other delegates and him immediately A B C accepted the resolution drafted by D the neutral states. No error. E A

B

C

16. Man cannot live by bread alone, or can he live A B C D without bread. No error. E 17. Having swam two-thirds of the distance across

A B C the English Channel, Dixon could not give up now. D No error. E

18. In the discussion, one speaker held that, since we

D

E

12. The girl who won the beauty contest is nowhere

A B near as beautiful as my mother was when she was C D a bride. No e rror. E

13. Sitting opposite my sister and me in the subway

A B were them same men who walked alongside us C D and tried to pinch us on Fifth Avenue. No error. E

14. Even if Detroit could provide nonpolluting cars by

A B the original deadline to meet prescribed Federal C standards for clean air, the effect in big cities would be slight because only new cars would be properly D equipped. No error. E

15. Of the two cars that the Smiths have, the Plymouth

A is, without any question, the cheapest to run. B C D No error. E

A live in a money-oriented society, the average B individual cares little about solving anyone’ s else C D problems. No error. E

19. Due to the meat boycott, the butchers were doing

A B about half of the business that they were doing C previous to the boycott. No error. D E

20. We requested the superintendent of the building

to clean up the storage room in the basement A B so that the children had enough space for their C D bicycles. No error. E 21. Lidocaine’s usefulness a s a local anesthetic

A B was discovered by two Swedish chemists who

repeatedly tested the drug’s effects on their C D bodies. No error. E 22. After he won the marathon relatively easily, he

A B decided to continue his training program and even to enter more races. No error. D E

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680 • SAT PRACTICE TEST 2 – SECTION 5 23. Learning by doing, long a guiding principal of

27. Everyone who attends a concert at the sports

24. The Watergate scandal may be a thing of the past

28. Our professor assigned us to write a short story,

A B C many educators, has been somewhat neglected D during the current back-to-basics boom. No error. E

A B but the Republicans will feel it’ s effects for a long C D time to come. No error. E

25. If we had began our vacation a day earlier, we

A B wouldn’ t have had so much trouble getting a plane C D reservation. No error. E

26. All of the class presidents but Jerry, Alice, and

A I were at the meeting to select the delegates for next B C month’ s convention. No error. D E

A B arena knows that they will be searched for drugs C before entering. No error. D E A B but I found I could not write one quick. No error. C D E

29.

One of the key suspects in the killing of a A B United States drug agent were captured early C D today by the police. No error. E

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SAT PRACTICE TEST 2 – SECTION 5 • 681 31. Sentence two should

Directions: The following passage is an early draft of an essay. Some parts of the passage need to be rewritten. Read the passage and select the best answers for the questions that follow. Some questions are about par ticular sentences or parts of sentences and ask you to improve sentence structure or word choice. Other questions ask you to consider organization and development. In choosing answers, follow the requirements of standard written English.

(A) be left as it is (B) begin with there instead of one (C) be joined to sentence one with and, omitting one was (D) omitted (E) begin with among the latter instead of one 32. Sentence three would be most improved by

(A) connecting it to sentence two with where and omitting in the sweat house (B) omitting adolescent (C) placing learning to be hunters before grown men and omitting who were (D) connecting it to sentence two with a semicolon (E) beginning with It was there

Questions 30–35 refer to the following passage. 1

The typical Miwok Indian village was compromised of both private family dwellings and communal dwellings. 2One was a men’s sweat house. 3In the sweat house, grown men and adolescent boys who were learning to be hunters sat around a small, open fire. 4Sometimes exchanging information and anecdotes and sometimes preparing themselves for the hunt to come by fasting, sweating and silent contemplation. 5 Occasionally a woman past childbearing age would be admitted to the sweat house. 6Adolescent girls learned to weave baskets and cook. 7When one of these older women was accepted into the membership of the Miwok men’s “clubhouse,” her acceptance was by popular acclaim and was based on her ability to tell entertaining or enlightening stories. 8As far as anthropologists know, no equal accommodations were made for males to enter the communal women’s house, which was set aside for menstruating or pregnant women.

33. Sentence four ought to

(A) be made into two sentences, the first to end with anecdotes (B) begin with Sometimes they exchanged (C) be improved by substituting once in a while for the second sometimes (D) be connected to sentence three with a comma (E) have or substituted for and sometimes after anecdotes 34. What is the best thing to do with sentence six?

(A) Place it in parentheses in sentence three, after adolescent boys. (B) Place it before sentence five. (C) Omit it. (D) Place it after sentence seven. (E) Leave it as it is.

30. What should be done with sentence one?

(A) It should be omitted. (B) Was compromised of should be changed to included. (C) It should be joined to sentence two with a semicolon. (D) It should not be changed. (E) The words was and of should be omitted.

35. Sentence eight should

(A) stop after house (B) be placed after sentence five (C) be made into two sentences, the first to end after house (D) begin a new paragraph (E) have ladies substituted for women


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SECTION 6 Time: 25 Minutes—Turn to Section 6 (page 656) of your answer sheet to answer the questions in this section. 18 Questions Directions: This section contains two types of questions. You have 25 minutes to complete both types. For questions 1–8, solve each problem and decide which is the best of the choices given. Fill in the corresponding circle on the answer sheet. You may use any available space for scratchwork.

Notes:




Distribution of U.S. Stamps in Harry’s Collection Commemoratives 52% Special Delivery 10% Postage Due 15% Air Mail 23%

1. If a, b are odd numbers, and c is even, which of the

following is an even number? (A) (B) (C) (D) (E) 2.

ab c a(b c) (a b) (b c) (a b) c a bc

According to the table above, of Harry’s collection, U.S. air mail stamps make up (A) (B) (C) (D) (E)

Distribution of Stamps in Harry’s Collection English French South American U.S.

22% 18% 25% 35%

4.00% 8.05% 15.50% 16.00% 21.35%


682

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3.

In the figure above, the sides of rectangle ABCD are parallel to the y-axis and x-axis as shown. If the rectangle is rotated clockwise about the origin through 90°, what are the new coordinates of B? (A) (B) (C) (D) (E)

4.

(3, 5) (3, 5) (3, 5) (5, 3) (5, 3)

5.

In the figure above, what is the sum of the degree measures of the marked angles? (A) (B) (C) (D) (E)

360° 720° 900° 1080° The answer cannot be determined from the information given.

The half-life of a certain radioactive substance is 6 hours. In other words, if you start with 8 grams of the substance, 6 hours later you will have 4 grams. If a sample of this substance contains x grams, how many grams remain after 24 hours? x (A) 32 x (B) 16 x (C) 8 (D) 2x (E) 4x

6.

Box A contains 3 cards, numbered 3, 4, and 5. Box B contains 3 cards, numbered 6, 7, and 8. If one card is drawn from each box and their sum is calculated, how many different sums are possible? (A) (B) (C) (D) (E)

eight seven six five four

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y

8.

If f(x) x x, which of the following is true? (A) (B) (C) (D) (E)

f(x) f(x) f(2x) 2f(x) f(x y) f(x) f(y) f(x) f(x) f(x y) 0

x

7.

Which of the following equations could not represent any of the above graphs? (A) (B) (C) (D) (E)

2y x y2 y 2x 6 y 2x 4 y4


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Directions: For Student-Produced Response questions 9–18, use the grids at the bottom of the answer sheet page on which you have answered questions 1–8. Each of the remaining 10 questions requires you to solve the problem and enter your answer by marking the circles in the special grid, as shown in the examples below. You may use any available space for scratchwork. 7 Answer: or 7/12 12

Grid in result.

➝

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Fraction line

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●


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2 Acceptable ways to grid .6666 … 3

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No question has a negative answer. 1 Mixed numbers such as 2 must be gridded as 2 2.5 or 5/2. (If

2

1 /

/

2


1 21 interpreted as , not 2 .) 2 2 9.

2

5

➝



Answer: 2.5

If f is a linear function and f(5) 6 and f(7) 8 what is the slope of the graph of f in the x- y plane?

●

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10.

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A bag contains exactly 4 blue marbles, 7 green marbles, and 8 yellow marbles. Fred draws marbles at random from the bag without replacement, one by one. If he does not look at the marbles he draws out, how many marbles will he have to draw out before he knows for sure that on his next draw he will have 1 marble for every color?


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11.

If 12 is the average (arithmetic mean) of 5 different integers, each integer 0, then what is the greatest that any one of t he integers could be?

13.

How many different pairs of parallel edges are there on a rectangular solid?

12.

A classroom has 12 seated students, 5 students at the board, and 7 empty seats. If 3 students leave the room, 2 enter, and all sit down, how many empty seats will there be?

14.

If the sum of 2r and 2r 3 is less than 11, find a possible value of r .


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15.

16.

Given the sum of two angles of a quadrilateral is 90°, find the average (arithmetic mean) of the measures of the other two angles. (Disregard the angle sign when gridding in your answer.)

17.

If x2 2xy y2 25, x y 0 and x y 1, then find the value of x.

Note: Figure is not drawn to scale.

18.

In the figure above, if sides LM and NM are cut apart from each other at point M creating 2 freeswinging segments and each is folded down to LN in the directions shown by the arrows, what will be the length, in meters, of the overlap of the 2 segments? (Disregard the thickness of the segments.)

If AD is a straight line segment in the figure above, find the value of x y.



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3.


(A) (B) (C) (D) (E)


4.

(A) enforce . . useful (B) end . . divisive (C) overcome . . unattractive (D) extend . . satisfactory (E) resolve . . acceptable B

C

2.

urgency . . lackadaisical flexibility . . hostile expectancy . . cautious dizziness . . visible disappointment . . fervent

D

5.

The foreman’s leniency, especially in being overfriendly, had its ––––––––––, one of which was ––––––––– workmanship. (A) (B) (C) (D) (E)

questionable distant immediate limited delayed

His current inability to complete his assignments in a timely and efficient manner has resulted in a feeling of ______ even in his most ______ backers. (A) (B) (C) (D) (E)

A

1.

The activities that interested Jack were those that provided him with _______ pleasure, like dancing, feasting, and partying.

The two performers taking the parts of shy, romantic teenagers were quite ______ in their roles even though they were in their forties. (A) (B) (C) (D) (E)

compensations . . unacceptable innuendoes . . superior drawbacks . . shoddy frequencies . . attractive cancellations . . mediocre

convincing flippant amateurish comfortable boring

Although the physical setup of the high school’s lunchroom seems rundown in many respects, it was enlarged and ________ quite recently. (A) (B) (C) (D) (E)

visited examined occupied renovated criticized


688

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The passages below are followed by questions based on their content; questions following a pair of related passages may also be based on the relationship between the paired passages. Answer the questions on the basis of what is stated or implied in the passages and in any introductory material that may be provided.

Questions 6–9 are based on the following passages.

8. Which aspects do the authors of both paragraphs

not discuss? (A) How the authors show the reader to accomplish what they advocate. (B) The consequences of not conforming to the author’s caution. (C) When to abide by the author’s admonition. (D) The dangers of not conforming to the author’s warnings. (E) The element of fear and timing.

Passage 1 To keep clear of concealment, to keep clear of the need of concealment, to do nothing which one might not do out in a crowded street of onlookers in the heart of a city at the middle of the day—I cannot say to me how more and more 5 it seems to me to be the glory of a young man’s life. It is an awful hour when the first necessity of hiding anything comes. The whole life is different thereafter. When there are questions to be feared and eyes to be avoided and subjects which must not be touched, then the bloom of life is 10 gone. Put off that day as long as possible. Put it off forever if you can. 1

Passage 2 Keeping things to yourself is an art. It is indeed a virtue to be able to hold back and not share what you would otherwise be tempted to convey. We must protect ourselves 15 from invaders that will use what we tell them and make us vulnerable to the slings and arrows of life. Who knows how what we tell them they will use for our detriment and what consequences will occur in all lives which touch us. There is no better time for concealment than today.

9.

Which lines describe analogies? (A) (B) (C) (D) (E)

lines 1 and 12 lines 2, 3, and 15 lines 6 and 18 lines 8 and 19 lines 9 and 16

6. The title below that best expresses the ideas of

both passages is: (A) (B) (C) (D) (E)

A time for concealment Fear and vulnerability A code for living Penalties for procrastination Youth vs. age

7. A description of the two paragraphs would be best

noted as (A) (B) (C) (D) (E)

Pro and con Contrasting and authoritarian Procrastinating and tenacious Optimistic and cautious Encouraging and dangerous


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10.

(A) the meaning of neoplasia (B) the inhibition of tumor metastasis by normal tissue (C) the transformation of benign tumors into malignant tumors (D) the manner in which malignant tumors behave in the body (E) the fate of malignant cells after they enter the bloodstream

The following passage describes the development of tumors, differentiating between the process of formation of malignant and benign ones.

5

10

15

20

25

30

35

40

45

50

Neoplasia, or the development of tumors, is the abnormal biological process in which some intrinsic cellular change within a group of normal cells produces a group of cells which no longer respond to the mechanisms which regulate normal cells. As a result, this group of cells increases in number but fails to achieve the specialized characteristics associated with normal cells. The degree to which neoplastic cells resemble their normal counterpart cells, both in appearance and behavior, allows us to classify tumors as either benign or malignant. Benign tumors look and behave like their normal tissue of origin, are usually slow-growing, are rarely fatal and remain localized. Malignant tumors, on the other hand, look very little like their tissue of origin and behave in such a manner that the animal which bears the tumor frequently succumbs. The characteristic which most strikingly separates malignant tumors from benign tumors is the ability of malignant cells to become widely disseminated and to establish secondary sites of tumor far distant from the original tumor. This process of widespread dissemination, which is called metastasis, is not well understood; however, some of the features of the process have been ascertained. Before metastasis can occur, the malignant cells must invade the surrounding normal tissue. Initial attempts to invade are inhibited by the normal tissue. With time, the neoplastic cells undergo changes which allow them to overcome this inhibition, and tumor cells leave the primary mass of tumor. The entire process of inhibition by normal tissue and the eventual breakdown of inhibition is undoubtedly complex. Malignant cells are characteristically less adhesive, one to another, than are normal cells. The outer membrane of the malignant cells contains less calcium than the membrane of normal cells. The malignant cell also acquires a greater negative electrical charge. After malignant cells have invaded the surrounding normal tissue, they ultimately enter the bloodstream where most of the cells die. Those cells which survive will form a metastasis at a distant site only if they can adhere to the wall of a small blood vessel. The factors which govern this adherence include the size of the malignant cell or a clump of these cells, the diameter of the blood vessel and the stickiness of the blood vessel wall. Stickiness of the blood vessel wall is at least partially due to the status of bloodclotting components in the blood. In addition to these mechanical considerations, some patterns of metastasis are explicable only on the basis of a receptive chemical environment or “soil” in which the malignant cell can grow. Finally, although a number of the characteristics of malignant neoplastic cells have been elucidated as described above, it still must be stated that many aspects of their behavior remain a mystery.

The main topic of this passage is

11.

Before malignant cells can be disseminated to widespread parts of the body, they must first (A) acquire new outer membrane characteristics (B) inhibit the lethal effects of components of the blood (C) penetrate the surrounding normal tissue (D) locate the proper chemical environment in which to grow (E) achieve sufficient size to become lodged in a blood vessel

12.

According to the passage, the property of a malignant cell that most greatly enhances its metastatic potential is (A) its ability to choose the proper “soil” (B) its ability to invade the surrounding tissue (C) the amount of calcium in the outer membrane of the cell (D) the extent of deviation from the appearance of a normal cell (E) its ability to attach itself to the wall of a small blood vessel

13.

It can be concluded from the passage that (A) benign tumors usually progress to malignant tumors (B) malignant cells reach distant tissues by routes yet to be ascertained (C) if the wall of a blood vessel is “sticky,” a tumor metastasis has a better chance to develop (D) the outer membrane of malignant cells is the same as that of normal cells (E) the pattern of metastasis of a particular tumor is predictable with considerable accuracy


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14.

According to this passage, characteristics that distinguish malignant neoplastic cells from normal cells include all of the following except (A) (B) (C) (D) (E)

their growth rate their physical appearance their outer membrane characteristics their normal tissue of origin their ability to invade surrounding tissue and metastasize

15.

The word “explicable” in line 45 means (A) (B) (C) (D) (E)

withdrawn with exception created explainable malignant


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Questions 16–24 are based on the following passage. The following passage is about the old Middle West and its influence on modern society.

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55

The old Middle West is gone. However, it still lives in song and story. Give most children the choice of visiting Valley Forge or Dodge City . . . Dodge City wins. It is more glamorous in their imagination than Valley Forge. The old Middle West developed a strong, compassionate people out of the hardships and suffering of the destructive blizzards of earlier generations—“northers” that swept over it with white clouds of blinding snow and ice—and southern winds that brought the black blizzards of dust storms. The Middle West is realistic about the nation’s domestic and international affairs. It views both with intense interest and anxiety, for it knows that—although stubborn resistance to change can lead to catastrophe—change often does have unforeseen ramifications. This caution is still—especially on political major questions—present in the modern Middle West and is its particular contribution to our national relationships. I think the Middle West’s strength is in its customary cautious approach to the day of reckoning in our complex industrial structure and what should be put forward for its solution. That solution will take time, for slapdash approaches never work. It took thirty years for our great country to recover from the upheaval of the Civil War. It took thirty years for our country to discard the Democrat policy that the way to settle economic troubles was with fiat money. It made inflation the prime issue in 1936. It still is. Our era has seen some fifty years of war and international tension piled on top of World War I, and enormous industrial development. The new West is more worldly minded than the old Middle West was, and, in general, is a balance between the East Coast—with alignment toward Europe and the Atlantic countries—and the West Coast—with its interests in Asian affairs. There is still a noticeable difference between the atmosphere in the Middle West and that of the Eastern states. It is more free and easy. There are not as many old families with local supremacy. The East’s “money power”—as the old Middle West called it—is now the “Establishment.” The parallel factor is the desire on the part of many heads of families in many lines of activity to change from the tensions and insecurity of life in the big cities to the pleasure and comfort that come from the security of living in smaller towns. In the Middle West, it has increasingly taken the form of people remaining in the smaller cities and giving them new life and intelligence. This has strengthened smaller communities and offset the flow of Middle Westerners to the big cities. There are, however, signs that cities in general are no longer content to be corrupt. There is pragmatic awakening that can mean a new leadership—with a growing understanding of their problems and responsibilities. This newly awakened urban leadership, joining the Midwest and small city leadership in the quest for stability, may just possibly be the salvation of the big cities.

60

65

70

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80

16.

That is a reversal of the trend that started some years ago that seemed to threaten the stagnation of the Middle West by the tide of migration to the big metropolitan areas. The Jews are almost the only people in America today— or, in the world, for that matter—that, during Passover, recall to the memory of the present generation their tremendous racial achievements, their leadership and their heroes of long ago. On the other hand, the freedom of communications— the easy movement of Americans around their great country—and the ease of changing occupations are remarkable in the United States. All contribute to breaking down ethnic and religious group prejudices. Possibly one reason we have so much difficulty in resolving our problems of a complex society is that we have tended to lose not only a sense of national identity, but a sense of pride in and a strong feeling for the special qualities of our local area. What Americans must find is a way to square their diversification, and the freedom upon which it is based, with the older sense of identity and of stability. Perhaps the contemporary Middle West offers the answer in its freer acceptance of people as they are, and as they are capable of becoming—a surviving characteristic of mutual helpfulness, willingness to accept change—not for change’s sake, but on its merits.

The author would agree that the “old Middle West” remains (A) (B) (C) (D) (E)

17.

The author feels that the strength of the Middle West lies in its (A) (B) (C) (D) (E)

18.

intact in only a few areas only in tales that are told unchanged in many small towns in spirit but is lost in practice a reality only to children who view it on television

tolerance of differences of opinion worldliness cautiousness free and easy atmosphere ability to recover from strife

A current trend that the author finds encouraging is (A) a gradual reduction in inflation (B) the increasing complexity of the national industrial structure (C) realism in domestic and international affairs (D) people staying in the smaller towns and cities (E) a growing sense of national identity


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19.

The character of the old Middle West was formed by

22.

(A) (B) (C) (D) (E)

I. weather hardships II. the Gold Rush of 1849 III. the Civil War (A) (B) (C) (D) (E) 20.

21.

I only II only III only I and II only I and III only

23.

lethargic anticipatory flippant practical governmental

24.

The author feels that we have had trouble in solving the problems of a complex society because (A) (B) (C) (D) (E)

of fiat money city governments are corrupt our cities are too large to be managed we have lost our attachment to local areas of the breakdown of ethnic and religious groups

a wealthy Middle West businessman a radical reformer a former political candidate a Middle West farmer a suburbanite

The word “diversification” in line 76 most likely refers to (A) (B) (C) (D) (E)

The word “pragmatic” in line 51 means (A) (B) (C) (D) (E)

It can be inferred that the author is

jobs income social stature intelligence race or religion

The author states that the following have been factors leading to the breakdown of ethnic and religious prejudices: I. Ease of communications II. Increased education at school and on the job III. Ease of changing occupations (A) (B) (C) (D) (E)

I only II only III only I and II only I and III only


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Notes:



1.


If x inversely varies with y and when x 5, y 4, find x when y 10. (A) (B) (C) (D) (E)

2.

2 3 4 5 cannot be determined

The projected sales of a music book per month is 4,000 at $1, 1,000 at $2, 250 at $4, and 160 at $5. If x is the price of the book, what are the expected sales per month in terms of x? (A) 1000/x2 (B) 1000/x (C) 2000/x2 (D) 4000/x2 (E) 4000/x


694

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SAT PRACTICE TEST 2 – SECTION 8 • 695 3. If x3 27, what is the value of x1/2?

5.

(A) 1/3

(A) (B) (C) (D) (E)

(B) 2 (C) 3 (D) 3/3 (E) 3/4

4.

The graph of y x 2 and y x2 4x 4 intersect at x 2, x 1 x 2 only x 1 only x 1, x 2 x 2, x 1

If f(x) 2x 3x what is the value of f(2)? (A) 9 (B) 10 (C) 11 (D) 12 (E) 13

6.

Points A, B, and C are on line m, as shown above, 4 such that AC AB. What is ratio of BC to AB? 3 1 (A) 4 1 (B) 3 1 (C) 2 2 (D) 3 (E) The answer cannot be determined from the given information.


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R (x, y) P (1,2) A (0,0)


In the figure above, AC is a straight line segment. Line segments are drawn from B to D, E, F, G, H, I, J, and K, respectively. Which of the following angles has a degree measure that can be found? (A) (B) (C) (D) (E)

8.

⬔FBG ⬔EBG ⬔DBG ⬔GBI ⬔GBJ

Given 8r 3s 12 and 7r 2s 9, find the value of 5(r s). (A) (B) (C) (D) (E)

9.

5 10 15 20 25

If points (1, 2) and (x, y) are on the line represented in the above diagram, which of the following could represent the value of x and y? (A) x 3, y 5 (B) x 4, y 8 (C) x 5, y 11 (D) x 6, y 15 (E) x 7, y 17

10.

If p is the average of x and y, and if q is the average of y and z, and if r is the average of x and z, then what is the average of x, y, and z? pqr (A) 3 pqr (B) 2 2 (C) (p q r) 3 (D) p q r 3 (E) (p q r) 2


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11.

In order to obtain admission into a special school program, all applicants must take a special exam, which is passed by three out of every five applicants. Of those who pass the exam, one-fourth are finally accepted. What is the percentage of all applicants who fail to gain admission into the program? (A) (B) (C) (D) (E)

12.

55 60 75 85 90

13.

In a certain school, special programs in French and Spanish are available. If there are N students enrolled in the French program, and M students in the Spanish program, including P students who enrolled in both programs, how many students are taking only one (but not both) of the language programs? (A) (B) (C) (D) (E)

NM NMP NMP N M 2P N M 2P

Which of the following represents a possible length of the hypotenuse of a triangle whose perpendicular sides are both integers? (A) 44 (B) 45 (C) 46 (D) 47 (E) 48 14. Lines ᐉ and n are parallel to each other, but line m

p is parallel to neither of the other two. Find q if p q 13. 13 (A) 5 12 (B) 5 7 (C) 6 1 (D) 5 (E) The answer cannot be determined from the information given.


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698 • SAT PRACTICE TEST 2 – SECTION 8 15. Ross wants to make up 3 letter combinations. He

16. The tables below show the number of uniforms

wants each combination to have exactly 3 of the following letters: A, B, C, and D. No letter can be used more than once. For example, “AAB” is not acceptable. What is the maximum number of such triplets that Ross can make up? (The order of the letters must be considered. Example: “ABC ” and “CBA” are acceptable triplets.)

ordered at two schools and the cost of the types of uniforms ordered in child and adult sizes. Find the maximum cost of all the uniforms in child sizes ordered at School B.

(A) (B) (C) (D) (E)

6 9 24 27 64

Number of Uniforms Ordered Type A

Type B

Type C

School A

20

50

40

School B

30

60

50

Cost of Uniforms Child

Adult

Type A

$9

$12

Type B

$10

$14

Type C

$11

$16

(A) (B) (C) (D) (E)

$30 $140 $1420 $1480 $1490


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3.


(A) (B) (C) (D) (E)


4.

(A) enforce . . useful (B) end . . divisive (C) overcome . . unattractive (D) extend . . satisfactory (E) resolve . . acceptable B

C

2.

He was _____ about a rise in the value of the stocks he had recently purchased and was eager to make a change in his investment portfolio.

Her fine reputation as a celebrated actress was _______ by her appearance in a TV soap opera. (A) (B) (C) (D) (E)

fearful unconcerned hesitant amused dubious

6.

Nature’s brute strength is never more ______ than during a major earthquake, when the earth shifts with a sickening sway. (A) (B) (C) (D) (E)

gradual . . sensation soothing . . mandate well-rehearsed . . diction superb . . aura chronic . . effervescence

D

5.

(A) (B) (C) (D) (E)

disdain . . denying revoke . . assigning abolish . . confining reduce . . diverting nourish . . planning

The dancer excelled neither in grace nor technique, but the _______ musical accompaniment gives the performance a(n) _______ of excellence. (A) (B) (C) (D) (E)

A

1.

Instead of providing available funds to education and thus ______ the incidence of crime, the mayor is _____ the funds to the building of more prisons.

The dictator’s slow, easy manner and his air of gentility _______ his firm intention to ensure no opposition to his planned ________ policies. (A) (B) (C) (D) (E)

frightening effective replaceable placating complete

enhanced blemished appreciated concluded intensified

revealed . . eager accepted . . professional belied . . drastic disregarded . . inane animated . . crude


699

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The two passages below are followed by questions based on their content and on the relationship between the two passages. Answer the questions on the basis of what is stated or implied in the passages and in any introductory material that may be provided.

Questions 7–19 are based on the following passages.

Passage 2 45

The following passages represent two different views of living—the views of living in the country and of living in the city. 50

Passage 1

5

10

15

20

25

30

35

40

The snow falls gently on our quiet meadow sloping down to Penobscot Bay, with spruce trees back against the gray of the water. A raven croaks from a nearby treetop. Two gulls sail over the house and squawk unintelligibly together. The only other sounds are the wood fire snapping, the kettle steaming on the stove and Pusso purring. There is no phone to ring, no radio to turn on, no television to watch. We need don no city disguise and ride subways, catch trains, attend cocktail parties or dinners. We can choose and make our own music, reread our favorite books, wear our old clothes, eat when and what we like from a well-stocked root cellar, or happily abstain from food, if we wish, the whole day. There is wood to cut, snow to shovel, mail to answer, but all in our own good time. No one is pushing, no one shoving, no one ordering about. There is no job to lose; we make our own jobs. Free men? Almost. A neighbor may amble in on snowshoes and bring us word of his horse’s health or wife’s pregnancy. Over a glass of cider we may talk of snowmobile incursions or hunters’ depredations. He may bring us a huge cabbage he has grown and we send him back with a bottle of our rosehips juice and a knitted doll for his little daughter. In our chat beside the fire we will probably not touch on the outside world, though we are not unaware of what stirs the nation. The newspaper, reaching us by mail, brings us echoes of an inconsequential election between two shadow-boxing candidates for an office no one should covet. We read that two high officials, the Episcopal Bishop of New York and the chief of the Soviet delegation to the United Nations, have separately been held up in daylight and robbed by armed men in Central Park. We learn that invaders are entering classrooms in Manhattan’s public schools and at knife or gunpoint relieving teachers of their cash and trinkets before their open-mouthed pupils. We thank our lucky stars that we live out in the wilderness, that we are not on congested streets and highways or clustered in high-rise city rookeries, with jangling noise and turmoil all about, that we are not in smog, that we can drink clean clear water, not fluoridized or chlorinated, from our bubbling spring, that our homegrown food is not stale, preserved or embalmed and bought from the supermarket. We are thankful for what the wilderness makes possible. Peace, progress, prosperity? We prefer peace, quiet, and frugality.

55

60

65

70

7.

You look out the window of your one-bedroom apartment and see swarms of people in the streets as if the day never ends. You live with the interminable sounds of the cars, trucks, and repair services and hassles encountered. But there is an excitement that makes you alive. You can leave your apartment at three in the morning and go to a coffee shop which remains open. You can lose your identity and forget about your problems by mingling during the day with the thousands of people roaming the streets. You may be walking right next to a famous celebrity or a lowly degenerate. But it doesn’t matter. It is the excitement that counts, the fact that you can call anybody anytime by phone, get up-tothe-minute news through radio or TV. You can choose from hundreds of international restaurants, and although the food may not be home-grown, you certainly have the exciting ambience of a packed restaurant with constant movement. You can choose from the best of hospitals and doctors, although it may take you some time to get an appointment with a doctor or get to the hospital because of traffic. But the noise, the inconveniences, the muggings, all this goes with the territory—with the excitement. You can always escape to the country by train, car, bus, or even plane if you need to. However, city living is certainly not for everyone. And your ability to live or even survive in a city depends on your temperament, your principles, your occupation and your interests. But for many, the tradeoff for a vibrant life, a pulse which never ends, and access to almost every cultural event almost at any time is certainly a lure to live in the city environment.

The general feeling running through Passage 1 is one of (A) (B) (C) (D) (E)

8.

guarded resentment tolerable boredom restless indecision peaceful satisfaction marked indifference

Which of the following is the most appropriate title for Passage 1? (A) (B) (C) (D) (E)

Winter in the Country The Frills Aren’t Needed Peace, Progress, and Prosperity Life Goes On A Lack of Conveniences


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9.

The author’s reference to “an inconsequential election between two shadow-boxing candidates” (lines 26–27) indicates that the author (A) (B) (C) (D) (E)

15. Which is more likely to be surprising to the respec-

tive author? (A) Passage 1 author: reading a headline in a newspaper: “Scientists Find Cancer Cure” (B) Passage 2 author: speaking with a famous movie celebrity in the street (C) Passage 2 author: finding a movie at two in the morning (D) Passage 1 author: seeing some people skip a few meals (E) Passage 2 author: hearing someone complain about city living

has no faith in politicians is opposed to professional prizefighting does not believe in having any elections prefers that people govern themselves is of the opinion that all elections are fixed

10. The author of Passage 1 states or implies that

(A) (B) (C) (D) (E)

there is no work to be done he is a completely free man his wife is pregnant he reads no newspapers he has a farm

16. The word “frugality” in line 44 means

(A) (B) (C) (D) (E)

11. Of the states below the location of the author’s

home in Passage 1 is most likely in the state of (A) (B) (C) (D) (E)

Arizona Florida Maine Louisiana Georgia

12. It can be inferred from Passage 2 that the author

believes that in the city (A) many people live in one-bedroom apartments (B) when eating out, you’ll never get home-grown food (C) you can meet rich and poor at the most expensive restaurants (D) losing one’s identity is considered a “plus” (E) friendliness is a “way of life” 13. The word “interminable” in line 47 means

(A) (B) (C) (D) (E)

loud harsh ongoing bright close

14. The passages differ in that

(A) in Passage 2, there is more of a tendency to qualify the good with the bad (B) in Passage 1 there are no hospitals in the village whereas there are many in Passage 2 (C) the author of Passage 1 believes that everyone should live in the country whereas in Passage 2 the author believes that everyone would do well in the city (D) in Passage 1 there are no post offices to deliver mail (E) in Passage 1 the author never reads newspapers whereas the author in Passage 2 is interested in up-to-the-minute news

17.

progress stinginess wastefulness poverty quiet

The word “don” in line 8 is related to (A) (B) (C) (D) (E)

motion purchasing goods clothing eating fishing

18. We can infer from the authors of each passage that

(A) the author of Passage 1 believes most news is bad whereas the author of Passage 2 believes most news is good (B) the author of Passage 1 believes politics and elections are useless whereas the author in Passage 2 believes they are necessary (C) the author of Passage 1 believes that city schools are dangerous and prefers not to have his or her children attend them whereas the author of Passage 2 may agree but accepts the situation (D) the author of Passage 1 believes only the parks in the cities are safe whereas the author of Passage 2 believes that crime “goes with the territory” (E) one author likes home-grown food, whereas the other does not

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19.

Which situation or condition is described or mentioned in one passage but not in the other? (i) The sociable and friendly nature of the people (ii) The positive effects of the environment (iii) The impossibility of attaining any news from outside locations or sources (A) (B) (C) (D) (E)

i only ii only iii only i and ii only i, ii, and iii


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SECTION 10 Time: 10 Minutes—Turn to Section 10 (page 657) of your answer sheet to answer the questions in this section. 14 Questions Directions: For each question in this section, select the best answer from among the choices given and fill in the corresponding circle on the answer sheet. 3. Every typist in the office except she was out sick at

least one day during the past month.

The following sentences test correctness and effectiveness of expression. Part of each sentence or the entire sentence is underlined; beneath each sentence are five ways of phrasing the underlined material. Choice A repeats the original phrasing; the other four choices are different. If you think the original phrasing produces a better sentence than any of the alternatives, select choice A; if not, select one of the other choices.

(A) (B) (C) (D) (E)

4. Sam is a professor of theoretical physics, while his

brothers are architects with outstanding reputa tions.

In making your selection, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, sentence construction, and punctuation. Your selection should result in the most effective sentence—clear and precise, without awkwardness or ambiguity.

(A) (B) (C) (D) (E)

Example:

5.

Laura Ingalls Wilder published her first book and she was sixty-five years old then. (A) and she was sixty-five years old then (B) when she was sixty-five (C) at age sixty-five years old (D) upon the reaching of sixty-five years (E) at the time when she was sixty-five A

B

C

D

except she except her excepting she but not her outside of her

E

while his brothers are architects also his brothers are architects his brothers architects as his brothers are architects and his brothers are architects

A reward was offered to whoever would return the dog to its owner. (A) to whoever would return the dog to its owner (B) to whomever would return the dog to its owner (C) to whosoever would return the dog to its owner (D) to whomsoever would return the dog to its owner (E) to whichever person would return the dog to its owner

6. Irregardless of the outcome of the battle, neither side

will be able to claim a decisive victory.

1. The bank robber approached the teller quietly, cau-

tiously, and in an unpretentious manner. (A) and in an unpretentious manner (B) and with no pretense (C) and by acting unpretentious (D) and by acting unpretentiously (E) and unpretentiously

(A) (B) (C) (D) (E)

Irregardless of the outcome of the battle Irregardless of how the battle ends Regardless of the outcome of the battle Despite the outcome of the battle Irregardless of the battle

2. The conduct of the judge with the accused seemed

very unfair to the jury. (A) (B) (C) (D) (E)

with the accused toward the accused as to the man who was accused and the accused as far as the accused was concerned


703

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7.

One of the finest examples of early Greek sculpture are to be found in the British Museum in London. (A) (B) (C) (D) (E)

8.

10.

When a student learns a foreign language, he must not only learn to speak and write it, but understand the culture of those who speak it. (A) but understand the culture of those who speak it (B) and he must understand the culture of those who speak it (C) he must understand the culture of those who speak it (D) but must also understand the culture of those who speak it (E) but in addition he must also understand the culture of those who speak it

11.

The paintings of Dali, like many artists, have been both applauded as great masterpieces and dismissed as rubbish.

are to be found in the British Museum were to be found in the British Museum are found in the British Museum is to be found in the British Museum are in the British Museum

W e w ere surprised at him canceling the order without giving any previous indication of his intentions. (A) We were surprised at him canceling the order without giving any previous indication of his intentions. (B) We were surprised that he canceled the order and didn’t tell anyone. (C) His canceling the order surprised us all. (D) We were surprised at his canceling the order without giving any previous indication of his intentions. (E) We were surprised at him canceling the order and not letting anyone know about it.

(A) (B) (C) (D) (E)

like many artists like most other artists like the paintings of many artists like many other paintings like those of many other artists

12. Because the sick man laid in bed for several months,

he developed pneumonia.

9. When going for an inter view, a high school

graduate should be prepared to answ er the questions that w ill be asked of him w ithout hesitation. (A) a high school graduate should be prepared to answer the questions that will be asked of him without hesitation. (B) a high school graduate should without hesitation be prepared to answer the questions that will be asked of him. (C) a high school graduate should be prepared without hesitation to answer the questions that will be asked of him. (D) a high school graduate should be prepared to answer without hesitation the questions that will be asked of him. (E) a high school graduate should be prepared to answer the questions without hesitation that will be asked of him.

(A) (B) (C) (D) (E)

Because the sick man laid in bed Because the sick man had laid in bed Because the sick man had lain in bed Because the sick man is laying in bed Because the sick man lies in bed

13.

The pollution bills recently passed by the House are different than those that were vetoed earlier (A) different than those (B) different from those (C) different to those (D) different from the earlier ones (E) different to the ones

14.

Neither you nor I are going to agree with the speaker; sometimes, however, it is a good idea to listen to someone whom one may disagree with. (A) (B) (C) (D) (E)

Neither you nor I are going to agree Neither of us are going to agree Neither you nor me is going to agree Neither you nor I am going to agree Neither I nor you am going to agree


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How Did You Do on This Test?

Step 1.

Go to the Answer Key on pages 706–708.

Step 2. For your “raw score,” calculate it using the directions on pages 709–710. Step 3. Get your “scaled score” for the test by referring to the Raw Score/Scaled Score Conversion Tables on pages 711–713. THERE’S ALWAYS ROOM FOR IMPROVEMENT!

705

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Page 706


Answer Key for the SAT Practice Test 2 (Math) Section 2

Section 6


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

D E D E C E E B B E E D E C E C E E E D

Number correct

Number incorrect

Correct Answer

Correct Answer 1 2 3 4 5 6 7 8

D C B E E A B D

Section 8

1 2 3 4 5 6 7 8

D B A B B D D B

Number correct

Number correct

Number incorrect

Number incorrect

Student-Produced Response Questions 9 24 10 10 11 2,300 12 11 13 125 14 25 15 4 16 3 17 36.2 18 7

Student-Produced Response Questions 1 9 /1, 1, 1.0, etc. 10 15 11 50 12 3 13 18 14 1.999, 1.998. . . . .001, or any number r such that 0 r 2 1 1 like , , etc. 2 4 15 135 16 100 17 3 18 4

Number correct

Number incorrect

Number correct

Number incorrect

Correct Answer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

A E D E D B C C B A D B D E C C

Number correct

Number incorrect

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Answer Key for the SAT Practice Test 2 (Critical Reading and Writing) Critical Reading

Section 4


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

E D D D C E B D E C B E D B A C B E D E C E E B


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

C D C E A C B A E D C E C D D B C D A D D C E E

Correct Answer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

E A D D B C D B A E C D C A A B C C A

Number correct

Number incorrect Number correct

Number correct

Number incorrect

Number incorrect

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Writing

Section 1

Essay score

Section 10

Section 5

Correct Answer

Correct Answer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

B E D B E C C A E E C B C E C C A D A D E A C C A B C D D B E A D C D

Number correct

Number incorrect

1 2 3 4 5 6 7 8 9 10 11 12 13 14

E B B E A C D D D D E C B D

Number correct

Number incorrect

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Scoring the SAT Practice Test 2 Check your responses with the correct answers on the previous pages. Fill in the blanks below and do the calculations to get your math, critical reading, and writing raw scores. Use the table to find your math, critical reading, and writing scaled scores.

Get Your Math Score

Get Your Critical Reading Score How many critical reading questions did you get right? Section 4: Questions 1–24

__________


__________


__________

Total

__________ (A)

How many math questions did you get right? Section 2: Questions 1–20

__________


__________


__________

Total

__________ (A)

How many critical reading questions did you get wrong? Section 4: Questions 1–24

__________


__________


__________

How many multiple-choice math questions did you get wrong?

Total

__________ (B)

0.25

__________


A⫺B

__________

__________


__________


__________

Total

__________ (B)

0.25

__________

A⫺B

__________ Math Raw Score

Round math raw score to the nearest whole number. ____________________ Use the Score Conversion Table to find your math scaled score. ____________________

Critical Reading Raw Score Round critical reading raw score to the nearest whole number. ____________________ Use the Score Conversion Table to find your critical reading scaled score. ____________________

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Page 710


Get Your Writing Score How many multiple-choice writing questions did you get right? Section 5: Questions 1–35

__________


__________

Total

__________ (A)

How many multiple-choice questions did you get wrong? Section 5: Questions 1–35

__________


__________

Total

__________ (B)

0.25

__________

A⫺B

__________ Writing Raw Score

Round writing raw score to the nearest whole number. ____________________ Use the Score Conversion Table to find your writing multiple-choice scaled score. ____________________ Estimate your essay score using the Essay Scoring Guide. ____________________ Use the SAT Score Conversion Table for Writing Composite to find your writing scaled score. You will need your Writing Raw Score and your Essay Score to use this table. ____________________

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SAT Score Conversion Table Raw Score


67



Raw Score


800

31

510

550

60

66

800

30

510

540

58

65

790

29

500

530

57

64

770

28

490

520

56

63

750

27

490

520

55

62

740

26

480

510

54

61

730

25

480

500

53

60

720

24

470

490

52

59

700

23

460

480

51

58

690

22

460

480

50

57

690

21

450

470

49

56

680

20

440

460

48

55

670

19

440

450

47

54

660

800

18

430

450

46

53

650

790

17

420

440

45

52

650

760

16

420

430

44

51

640

740

15

410

420

44

50

630

720

14

400

410

43

49

620

710

80

13

400

410

42

48

620

700

80

12

390

400

41

47

610

680

80

11

380

390

40

46

600

670

79

10

370

380

39

45

600

660

78

9

360

370

38

44

590

650

76

8

350

360

38

43

590

640

74

7

340

350

37

42

580

630

73

6

330

340

36

41

570

630

71

5

320

330

35

40

570

620

70

4

310

320

34

39

560

610

69

3

300

310

32

38

550

600

67

2

280

290

31

37

550

590

66

1

270

280

30

36

540

580

65

0

250

260

28

35

540

580

64

1

230

240

27

34

530

570

63

2

210

220

25

33

520

560

62

3

200

200

23

32

520

550

61

4

200

200

20

Math Scaled Score

Math Scaled Score

and below This table is for use only with the test in this book. *This Writing multiple-choice score is reported on a 20–80 scale. Use the SAT Score Conversion Table for Writing Composite for the total writing scaled score.

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SAT Score Conversion Table for Writing Composite Writing MultipleChoice Raw Score

0

1

2

Essay Raw Score 3

4

5

6

12

200

200

200

210

240

270

300

11

200

200

200

210

240

270

300

10

200

200

200

210

240

240

300

9

200

200

200

210

240

270

300

8

200

200

200

210

240

270

300

7

200

200

200

210

240

270

300

6

200

200

200

210

240

270

300

5

200

200

200

210

240

270

300

4

200

200

200

230

270

300

330

3

200

210

230

250

290

320

350

2

200

230

250

280

310

340

370

1

210

240

260

290

320

360

380

0

230

260

280

300

340

370

400

1

240

270

290

320

350

380

410

2

250

280

300

330

360

390

420

3

260

290

310

340

370

400

430

4

270

300

320

350

380

410

440

5

280

310

330

360

390

420

450

6

290

320

340

360

400

430

460

7

290

330

340

370

410

440

470

8

300

330

350

380

410

450

470

9

310

340

360

390

420

450

480

10

320

350

370

390

430

460

490

11

320

360

370

400

440

470

500

12

330

360

380

410

440

470

500

13

340

370

390

420

450

480

510

14

350

380

390

420

460

490

520

15

350

380

400

430

460

500

530

16

360

390

410

440

470

500

530

17

370

400

420

440

480

510

540

18

380

410

420

450

490

520

550

19

380

410

430

460

490

530

560

20

390

420

440

470

500

530

560

21

400

430

450

480

510

540

570

22

410

440

460

480

520

550

580

23

420

450

470

490

530

560

590

24

420

460

470

500

540

570

600

25

430

460

480

510

540

580

610

712

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Page 713


Writing MultipleChoice Raw Score

0

1

2

Essay Raw Score 3

4

5

6

26

440

470

490

520

550

590

610

27

450

480

500

530

560

590

620

28

460

490

510

540

570

600

630

29

470

500

520

550

580

610

640

30

480

510

530

560

590

620

650

31

490

520

540

560

600

630

660

32

500

530

550

570

610

640

670

33

510

540

550

580

620

650

680

34

510

550

560

590

630

660

690

35

520

560

570

600

640

670

700

36

530

560

580

610

650

680

710

37

540

570

590

620

660

690

720

38

550

580

600

630

670

700

730

39

560

600

610

640

680

710

740

40

580

610

620

650

690

720

750

41

590

620

640

660

700

730

760

42

600

630

650

680

710

740

770

43

610

640

660

690

720

750

780

44

620

660

670

700

740

770

800

45

640

670

690

720

750

780

800

46

650

690

700

730

770

800

800

47

670

700

720

750

780

800

800

48

680

720

730

760

800

800

800

49

680

720

730

760

800

800

800

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CHART FOR SELF-APPRAISAL BASED ON THE PRACTICE TEST YOU HAVE JUST TAKEN The Self-Appraisal Chart below tells you quickly where your SAT strengths and weaknesses lie. Check or circle the appropriate box in accordance with the number of your correct answers for each area of the Practice Test 2 you have just taken.

Writing (Multiplechoice) EXCELLENT GOOD FAIR POOR VERY POOR

42–49 37–41 31–36 20–30 0–19

Sentence Completions 16–19 13–15 9–12 5–8 0–4


Math Questions*

40–48 35–39 26–34 17–25 0–16

44–54 32–43 27–31 16–26 0–15

* Sections 2, 6, and 8 only Note: In our tests, we have chosen to have Section 3 as the experimental section. We have also chosen it to be a math section since we felt that students may need more practice in the math area than in the verbal area. Note that on the actual SAT you will take, the order of the sections can vary and you will not know which one is experimental, so it is wise to answer all sections and not to leave any section out.

SAT VERBAL AND MATH SCORE/PERCENTILE CONVERSION TABLE Critical Reading and Writing

Math

SAT scaled Percentile verbal score rank 800 . . . . . . . . . . . . . . . . 99.7 790 . . . . . . . . . . . . . . . . 99.5 740–780 . . . . . . . . . . . . 99 700–730 . . . . . . . . . . . . 97 670–690 . . . . . . . . . . . . 95 640–660 . . . . . . . . . . . . 91 610–630 . . . . . . . . . . . . 85 580–600 . . . . . . . . . . . . 77 550–570 . . . . . . . . . . . . 68 510–540 . . . . . . . . . . . . 57 480–500 . . . . . . . . . . . . 46 440–470 . . . . . . . . . . . . 32 410–430 . . . . . . . . . . . . 21 380–400 . . . . . . . . . . . . 13 340–370 . . . . . . . . . . . . 6 300–330 . . . . . . . . . . . . 2 230–290 . . . . . . . . . . . . 1 200–220 . . . . . . . . . . . . 0–0.5

SAT scaled Percentile math score rank 800 . . . . . . . . . . . . . . . . 99.5 770–790 . . . . . . . . . . . . 99.5 720–760 . . . . . . . . . . . . 99 670–710 . . . . . . . . . . . . 97 640–660 . . . . . . . . . . . . 94 610–630 . . . . . . . . . . . . 89 590–600 . . . . . . . . . . . . 84 560–580 . . . . . . . . . . . . 77 530–550 . . . . . . . . . . . . 68 510–520 . . . . . . . . . . . . 59 480–500 . . . . . . . . . . . . 48 450–470 . . . . . . . . . . . . 37 430–440 . . . . . . . . . . . . 26 390–420 . . . . . . . . . . . . 16 350–380 . . . . . . . . . . . . 8 310–340 . . . . . . . . . . . . 2 210–300 . . . . . . . . . . . . 0.5 200 . . . . . . . . . . . . . . . . 0

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Section 1—Essay The following are guidelines for scoring the essay.

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The SAT Scoring Guide Score of 6

Score of 5

Score of 4



















Score of 3

Score of 2

Score of 1




















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1. Choice D is correct.

Multiply 1 by y, to get

Given that 500w 3 700

3 y y (7)y y

1

(Use Strategy 13: Find an unknown by dividing.)

3 y 7y 3 6y 3 y 6 1 y 2

Divide 1 by 500, giving 5 00w 3 700 500 500 (Use Strategy 19: Factor and reduce first. Then multiply.)

(Math Refresher

3 7 1 00 w 5 10 0 21 w 5 (Math Refresher

ⱅ406)

3. Choice D is correct. (Use Strategy 2: Translate

from words to algebra.) x is a multiple of 9, gives

ⱅ406)

x ε {9, 18, 27, 36, 45, 54, . . . . . . } x is a multiple of 12, gives x ε {12, 24, 36, 48, 60, 72, . . . . . . }

2. Choice E is correct.

3y Given: 7 y

1

1 2

The smallest value that appears in both sets 1 and 2 is 36.

(Use Strategy 13: Find an unknown by multiplying.)

(Logical Reasoning)

717

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4.


Substituting 6 into 4 , we get OD OC 10

Method 1: (r s) (t s) (s r) (s t)

Given:

1

Substituting 2 , 7 , and 8 into 1 , we get 21 10 CB 4 21 14 CB 7 CB

(Use Strategy 17: Use the given information effectively.) Recognizing that (s r) 1(r s) (s t) 1(t s)

2 3

Substituting 2 and 3 into 1 , we get (r s)(t s) [1(r s)] [1(t s)] (r s)(t s) (r s)(t s) 2(r s)(t s) Method 2: Given: (r s)(t s) (s r)(s t)

(Math Refresher

9

Area of square II (CB)2 Area of square II 72 (From 9 ) Area of square II 49 (Math Refresher

ⱅ410 and ⱅ303)


Given: 1

Multiply both pairs of quantities from 1 , giving rt rs st s2 s2 st rs rt 2rt 2rs 2st 2s2 2(rt rs st s2) 2[r(t s) s(t s)] 2(r s)(t s)

8

1 cup 100 grams 1 cake 75 grams 1 pie 225 grams

1 2 3

Using 1 , we get 4 cups 4 (100 grams) 4 cups 400 grams

ⱅ409)

4

(Using Strategy 8: When all choices must be tested, start with E and work backward.) 2 cakes and 1 pie is Choice E. Substituting 2 and 3 in 5 , we get 2(75 grams) 225 grams 150 grams 225 grams 375 grams

5

6

Since 6 is less than 4 , there is enough in 4 cups. So Choice E is correct. (Math Refresher

ⱅ121 and ⱅ431)


5.

Choice C is correct. We want to find the area of the middle square, which is (CB)2. (Use Strategy 3: The whole equals the sum of its parts.) OA OC CB BA

1

From the diagram, we get OA 21 AE 4 OD 10

2 3 4

Since each figure is a square, we get BA AE OC OD

5 6

Substituting 5 into 3 , we get AE BA 4

7

y2 y1 where (x 1 , y 1 ) and I: Slope is defined as x2 x1 (x2, y2) are points on the line. Thus here 0 x1, a y1, a x2, and 0 y2 y2 y1 oa Thus 1: I is therefore true. x2 x1 ao II: The triangle created above is an isosceles right . Thus II is true. triangle with sides a, a, a2 III: In an isosceles right triangle, the interior angles of the triangle are 90–45–45 degrees. Thus III is true. (Math Refresher

ⱅ416, ⱅ411, ⱅ509)

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SAT PRACTICE TEST 2 – SECTION 2 ANSWERS • 719 8. Choice E is correct. Choice A is incorrect: On the

number line b is to the left of 2 so this implies that b is less than 2 (written as b 2). Since b 2, b is certainly less than 1 (written as b 1). Thus Choice A is incorrect. Choice B is false because if b 2, the absolute value of b (denoted as b) must be greater than 2. Choice C is false: c is positive (c 3 0) so c c, since c is negative. Choice D is false: Since a and b are negative numbers and since a b, a b, Choice E is correct and Choice D is incorrect. (Math Refresher 419, 615, 410, 129) 9. Choice B is correct. (Use Strategy 2: Translate

from words to algebra.) We are told: 1

(Use Strategy 1: Cancel expressions that appear on both sides of an equation.) Each side contains an A, A 1, and A 2. Canceling each of these from each side, we get 1 A 2 A A 1 A 8 A A 2 A 3.

(Math Refresher

given information effectively.) Given: w 7r 6r 5r 4r 3r Then, w 25r

1

We are told we must add something to w so that the resulting sum will be divisible by 7 for every positive integer r. Check the choices. (Use Strategy 8: Start with Choice E.) Add 3r to 1 25r 3r 28r 7(4r) will always be divisible by 7. Thus, Choice E is correct. (Math Refresher

A8A1A2 AA1A2A3

Thus, 8 A 3 5A

11. Choice E is correct. (Use Strategy 17: Use the

ⱅ431)

12. Choice D is correct. To obtain the maximum num-

ber of members of S, choose the numbers as small as possible; hence 1 3 5 7 9 1 1 1 3 1 5 64 Hence, the maximum is 8. (Math Refresher

ⱅ801)

13. Choice E is correct. I, II, and III are correct.

ⱅ406)

Examples: (23)2 26 64, 232 23 22 32, (2 3)2 22 32 36. (Math Refresher

ⱅ429)

14. Choice C is correct. (Use Strategy 2: Translate

from words to algebra.) The number of hours from 7:00 A.M. to 5:00 P.M. is 10. 10. Choice E is correct. (Use Strategy 11: New defi-

nitions lead to easy questions.) By the definition of a move, every 4 moves brings each hand back to 12. Thus, after 4, 8, 12, and 16 moves, respectively, each hand is at 12. Hand A, moving counterclockwise, moves to 9 on its 17th move. Hand B, moving clockwise, moves to 3 on its 17th move. (Logical Reasoning)

The number of hours from 1:00 P.M. to 7:00 P.M. is 6. He worked 10 hours for 3 days and 6 hours for 3 days. Thus, Total Hours 3(10) 3(6) 30 18 Total hours 48 Total Earnings Hours worked Hourly rate Given: He earns $10 per hour Substituting 1 and 3 into 2 , we get Total Earnings 48 $10 Total Earnings $480 (Math Refresher

1 2 3

ⱅ200 and ⱅ406)

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720 • SAT PRACTICE TEST 2 – SECTION 2 ANSWERS 16. Choice C is correct. In ascending order, the wages

for the six days are: 35 35 40 45 60 75

15. Choice E is correct. (Use Strategy 3: The whole

equals the sum of its parts.) The sum of the angles in a Δ 180. For the small triangle we have 120 a a 180 120 2a 180 2a 60 a 30

ⱅ

ⱅ

17. Choice E is correct. (Use Strategy 11: Use new

definitions carefully.) (Use Strategy 8: When all choices must be tested, start with E and work backward.) 1

For Δ RST, we have 100 mSRT mSTR 180 From the diagram, we get

The median is the middle number. But wait! There is no middle number. So we average the two middle numbers, 40 and 45, to get 42.5. The mode is the number appearing most frequently, that is, 35. So 42.5 35 7.5. (Math Refresher 601a, 601b)

2

Given:

a

b

a1 b1

Choice E:

5

3

51 6 3 31 2

mSRT a b

3

Choice E is the only choice with a > b.

mSTR a b

4

Therefore, it must be the largest. The remaining choices are shown below. 41 5 1 Choice D: 4 5 1 51 4 4

Substituting 3 and 4 into 2 , we get 100 a b a b 180 100 2a 2b 180 2a 2b 80

5

Choice C: 3

5

31 4 1 51 4

Choice B:

3

3

31 4 2 31 2

Choice A: 2

3

21 3 1 1 31 2 2

Substituting 1 into 5 , we get 2(30) 2b 80 60 2b 80 2b 20 b 10 (Math Refreshers Question 16

ⱅ505 and ⱅ406)

(Math Refresher

ⱅ431)


given information effectively.)

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1 We know that Area of Δ base height 1 2 We are given that RS ST an integer 2 Substituting 2 into 1 , we get 1 Area ΔRST (An integer) (same integer) 2 1 Area ΔRST (An integer)2 2

3

Multiplying 3 by 2, we have 2(Area ΔRST) (An integer)2

4 cubic feet Number of cubes .001 cubic feet 4 Number of cubes .001 Multiplying numerator and denominator by 1,000, we get 4 1,000 Number of cubes .001 1,000 4,000 Number of cubes 1

4

(Use Strategy 8: When all choices must be tested, start with E and work backward.)

4,000 Number of cubes (Math Refresher

Substituting Choice E, 20, into 4 , we get 2(20) (An integer)2 40 (An integer)2 5 is not possible, since 40 isn’t the square of an integer. (Math Refresher

ⱅ312 and ⱅ313)


5

from words to algebra.) (Use Strategy 17: Use the given information effectively.)

ⱅ307, ⱅ406, and ⱅ431)


given information effectively.) Volume of rectangler solid l w h

1

Substituting the given dimensions into 1 , we get Volume of solid 2 feet 2 feet 1 foot Volume of solid 4 cubic feet Volume of cube (edge)3 Substituting edge .1 foot into 3 , we get Volume of cube (.1 foot)3 Volume of cube .001 cubic feet

Given the perimeter of the square 40 Thus, 4(side) 40 side 10

2 3

1

A side of the square length of diameter of circle. 4

(Use Strategy 3: The whole equals the sum of its parts.) Since the volume of the rectangular solid must equal the sum of the small cubes, we need to know Volume of rectangular solid Number of cubes 5 Volume of cube Substituting 2 and 4 into 5 , we get Volume of rectangular solid Number of cubes Volume of cube

Since (radius)

Thus, diameter 10 from 1 diameter 2

10 2 (radius) 5 radius Area of a circle pr 2 Substituting 2 into 3 , we have Area of circle p r 2 Area of circle 25p (Math Refresher

2 3

ⱅ303 and ⱅ310)

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becomes

from words to algebra.)

15 16 x 20 20

Let n the number. n3 Then 6 4

(Use Strategy 15: Certain choices may be easily eliminated.)

Multiplying both sides by 4, we have

13 Choice B can be instantly eliminated. 20

n3 4 (6)4 4

n 3 24 n 21 (Math Refresher

16 Choice D can be instantly eliminated. 20

ⱅ200)

Change both fractions to 40ths to compare Choice C. Thus,

2. Choice C is correct. (Use Strategy 17: Use the

30 32 x 40 40

given information effectively.) 3 4 Given: x 4 5

31 Choice C is a possible value of x. 40

Change both fractions to fractions with the same denominator. Thus,

(Math Refresher

3 4 x 4 5

722

ⱅ108 and ⱅ419)

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The more sophisticated way of doing this is to use Strategy 8: When all choices must be tested, start with Choice E and work backward.

3. Choice B is correct. (Use Strategy 2: Translate

from words to algebra.) Perimeter of a square 4 side. We are given that Perimeter 20 meters

1 2

Choice E is x2 + x + 2. Now factor: x2 + x + 2 = x(x + 1) + 2.

Substituting 2 into 1 , we get 20 meters 4 side 5 meters side Area of square (side)2

Note that since x is an integer, x(x + 1) is always the product of an even integer multiplied by an odd integer. So x(x + 1) is 2 times an integer and therefore even. + 2 is even so x(x + 1)+ 2 is even. And since x(x + 1) + 2 = x2 + x + 2, x2 + x + 2 is even.

3 4

Substituting 3 into 4 , we get Area of square (5 meter)2 Area of square 25 square meters (Math Refresher

ⱅ303)

(Math Refresher #409) 6. Choice A is correct. (Use Strategy 17: Use the



Given: ax r


by r 1

Given: 80 a 32 b

2

The quick method is to substitute 1 into 2 , giving by ax 1

Subtract a from both sides, getting 80 a 32 b a a 80 32 b a

by 1 ax by 1 a x

Add 32 to both sides, giving 80 32 b a 32 32 112 ba (Math Refresher

1

(Math Refresher

ⱅ406)

7.

5. Choice E is correct. (Use Strategy 8: When all

choices must be tested, start with E and work backward.) Choice E is x2 x 2

ⱅ431 and ⱅ406)

Choice B is correct. Let the capacity of container B be x. Then the capacity of container A will be 2x, and that of container C will be 3x. The amount poured into container C is equal to half of 2x x x 4x 2x plus one-third of x, or x . 2 3 3 3 Dividing this amount by the total capacity of container C, we find the fraction that was filled: 4x 4 3 . 9 3x

(Use Strategy 7: Use specific number examples.) Let x 3 (an odd positive integer)

(Math Refresher

Then x2 x 2 32 3 2 932 14 (an even result) Now let x 2 (an even positive integer) Then x2 x 2 22 2 2 422 8 (an even result)

8.

Choice D is correct. In 12 seconds, the wheel travels through 2 revolutions (since 12 seconds is 1/5 of the minute it would take for ten revolutions). Since this distance is equal to 16 feet, the wheel travels 8 feet per revolution; thus, 8 feet must be the circumference of the wheel. To find the diameter, we divide this figure by p (because the circumference of a circle is p times its diameter). Thus, 8 the diameter is feet. p

Whether x is odd or even, Choice E is even. (Math Refresher

ⱅ 431)

ⱅ406)

(Math Refresher

ⱅ310)

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724 • SAT PRACTICE TEST 2 – SECTION 3 ANSWERS 9. 24 (Use Strategy 2: Translate from words to

algebra.)

13. 125 (Use Strategy 18: Remember the isos-

celes triangle.) Since AB BC in Δ ABC, it is isosceles, and the opposite angles are equal. So

Let n the number We are given:

1

m A y

5 3 n n 3 8 4

1

(Use Strategy 13: Find unknowns by multiplication.) Multiply 1 by 8. We get

m A y 90 180

Subtracting 90 from both sides gives

5 3 8 n 8 n 3 8 4

2

m A y 90

24 5n n 24 4

From 1 , the angles are , so substituting y for A in 2 gives

5n 6n 24 24 n

(Use Strategy 3: The whole equals the sum of its parts.) The sum of the angles in a triangle is 180 , so

y y 90 2y 90 2 2

(Answer)

(Math Refresher

ⱅ200 and ⱅ406)

3

y 45

10. 10 (Use Strategy 11: Use new definitions care-

x° is a central angle, so it is measured by the intercepted arc AD.

Gruber's Complete SAT Guide 2009

Gruber's Complete SAT Guide 2009 (Gruber's Complete SAT Guide -12th Edition)

Gruber's Complete SAT Writing Workbook

Gruber's Complete SAT Reading Workbook

Gruber's Complete SAT Math Workbook

McGraw-Hill's SAT, 2009 Edition (Mcgraw Hill's Sat)

Frommer's London 2009 (Frommer's Complete)

Frommer's Paris 2009 (Frommer's Complete)

Frommer's Spain 2009 (Frommer's Complete)

Frommer's Toronto 2009 (Frommer's Complete)

Frommer's Toronto 2009 (Frommer's Complete)

Frommer's Bahamas 2009 (Frommer's Complete)

Frommer's Italy 2009 (Frommer's Complete)

Frommer's Germany 2009 (Frommer's Complete)

Frommer's Mexico 2009 (Frommer's Complete)

Frommer's Australia 2009 (Frommer's Complete)

Frommer's Chicago 2009 (Frommer's Complete)

Frommer's London 2009 (Frommer's Complete)

Frommer's Hawaii 2009 (Frommer's Complete)

Frommer's Caribbean 2009 (Frommer's Complete)

Frommer's Hawaii 2009 (Frommer's Complete)

Frommer's London 2009 (Frommer's Complete)

Frommer's Maui 2009 (Frommer's Complete)

Frommer's California 2009 (Frommer's Complete)

Frommer's Arizona 2009 (Frommer's Complete)

Frommer's Hawaii 2009 (Frommer's Complete)

Frommer's Alaska 2009 (Frommer's Complete)

Frommer's Seattle 2009 (Frommer's Complete)

Frommer's Spain 2009 (Frommer's Complete)

Frommer's Toronto 2009 (Frommer's Complete)

SAT Success 2004 (Sat Success)

Gruber's Complete SAT Guide 2009